\begin{funcdesc}{Chi}{...}\index{Chi}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{Chi_e}{...}\index{Chi_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{Ci}{...}\index{Ci}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{Ci_e}{...}\index{Ci_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{Shi}{...}\index{Shi}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{Shi_e}{...}\index{Shi_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{Si}{...}\index{Si}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{Si_e}{...}\index{Si_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{airy_Ai}{...}\index{airy_Ai}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1

 Argument 2 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX

\end{funcdesc}

\begin{funcdesc}{airy_Ai_deriv}{...}\index{airy_Ai_deriv}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1

 Argument 2 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX

\end{funcdesc}

\begin{funcdesc}{airy_Ai_deriv_e}{...}\index{airy_Ai_deriv_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

 Argument 2 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX
The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{airy_Ai_deriv_scaled}{...}\index{airy_Ai_deriv_scaled}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1

 Argument 2 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX

\end{funcdesc}

\begin{funcdesc}{airy_Ai_deriv_scaled_e}{...}\index{airy_Ai_deriv_scaled_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

 Argument 2 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX
The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{airy_Ai_e}{...}\index{airy_Ai_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

 Argument 2 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX
The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{airy_Ai_scaled}{...}\index{airy_Ai_scaled}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1

 Argument 2 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX

\end{funcdesc}

\begin{funcdesc}{airy_Ai_scaled_e}{...}\index{airy_Ai_scaled_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

 Argument 2 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX
The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{airy_Bi}{...}\index{airy_Bi}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1

 Argument 2 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX

\end{funcdesc}

\begin{funcdesc}{airy_Bi_deriv}{...}\index{airy_Bi_deriv}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1

 Argument 2 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX

\end{funcdesc}

\begin{funcdesc}{airy_Bi_deriv_e}{...}\index{airy_Bi_deriv_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

 Argument 2 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX
The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{airy_Bi_deriv_scaled}{...}\index{airy_Bi_deriv_scaled}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1

 Argument 2 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX

\end{funcdesc}

\begin{funcdesc}{airy_Bi_deriv_scaled_e}{...}\index{airy_Bi_deriv_scaled_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

 Argument 2 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX
The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{airy_Bi_e}{...}\index{airy_Bi_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

 Argument 2 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX
The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{airy_Bi_scaled}{...}\index{airy_Bi_scaled}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1

 Argument 2 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX

\end{funcdesc}

\begin{funcdesc}{airy_Bi_scaled_e}{...}\index{airy_Bi_scaled_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

 Argument 2 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX
The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{airy_zero_Ai}{...}\index{airy_zero_Ai}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{airy_zero_Ai_deriv}{...}\index{airy_zero_Ai_deriv}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{airy_zero_Ai_deriv_e}{...}\index{airy_zero_Ai_deriv_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{airy_zero_Ai_e}{...}\index{airy_zero_Ai_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{airy_zero_Bi}{...}\index{airy_zero_Bi}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{airy_zero_Bi_deriv}{...}\index{airy_zero_Bi_deriv}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{airy_zero_Bi_deriv_e}{...}\index{airy_zero_Bi_deriv_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{airy_zero_Bi_e}{...}\index{airy_zero_Bi_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{angle_restrict_pos}{...}\index{angle_restrict_pos}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{angle_restrict_pos_err_e}{...}\index{angle_restrict_pos_err_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{angle_restrict_symm}{...}\index{angle_restrict_symm}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{angle_restrict_symm_err_e}{...}\index{angle_restrict_symm_err_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{atanint}{...}\index{atanint}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{atanint_e}{...}\index{atanint_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_I0}{...}\index{bessel_I0}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_I0_e}{...}\index{bessel_I0_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_I0_scaled}{...}\index{bessel_I0_scaled}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_I0_scaled_e}{...}\index{bessel_I0_scaled_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_I1}{...}\index{bessel_I1}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_I1_e}{...}\index{bessel_I1_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_I1_scaled}{...}\index{bessel_I1_scaled}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_I1_scaled_e}{...}\index{bessel_I1_scaled_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_In}{...}\index{bessel_In}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_In_e}{...}\index{bessel_In_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_In_scaled}{...}\index{bessel_In_scaled}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_In_scaled_e}{...}\index{bessel_In_scaled_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_Inu}{...}\index{bessel_Inu}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_Inu_e}{...}\index{bessel_Inu_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_Inu_scaled}{...}\index{bessel_Inu_scaled}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_Inu_scaled_e}{...}\index{bessel_Inu_scaled_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_J0}{...}\index{bessel_J0}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_J0_e}{...}\index{bessel_J0_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_J1}{...}\index{bessel_J1}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_J1_e}{...}\index{bessel_J1_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_Jn}{...}\index{bessel_Jn}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_Jn_e}{...}\index{bessel_Jn_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_Jnu}{...}\index{bessel_Jnu}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_Jnu_e}{...}\index{bessel_Jnu_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_K0}{...}\index{bessel_K0}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_K0_e}{...}\index{bessel_K0_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_K0_scaled}{...}\index{bessel_K0_scaled}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_K0_scaled_e}{...}\index{bessel_K0_scaled_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_K1}{...}\index{bessel_K1}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_K1_e}{...}\index{bessel_K1_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_K1_scaled}{...}\index{bessel_K1_scaled}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_K1_scaled_e}{...}\index{bessel_K1_scaled_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_Kn}{...}\index{bessel_Kn}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_Kn_e}{...}\index{bessel_Kn_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_Kn_scaled}{...}\index{bessel_Kn_scaled}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_Kn_scaled_e}{...}\index{bessel_Kn_scaled_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_Knu}{...}\index{bessel_Knu}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_Knu_e}{...}\index{bessel_Knu_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_Knu_scaled}{...}\index{bessel_Knu_scaled}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_Knu_scaled_e}{...}\index{bessel_Knu_scaled_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_Y0}{...}\index{bessel_Y0}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_Y0_e}{...}\index{bessel_Y0_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_Y1}{...}\index{bessel_Y1}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_Y1_e}{...}\index{bessel_Y1_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_Yn}{...}\index{bessel_Yn}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_Yn_e}{...}\index{bessel_Yn_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_Ynu}{...}\index{bessel_Ynu}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_Ynu_e}{...}\index{bessel_Ynu_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_i0_scaled}{...}\index{bessel_i0_scaled}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_i0_scaled_e}{...}\index{bessel_i0_scaled_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_i1_scaled}{...}\index{bessel_i1_scaled}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_i1_scaled_e}{...}\index{bessel_i1_scaled_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_i2_scaled}{...}\index{bessel_i2_scaled}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_i2_scaled_e}{...}\index{bessel_i2_scaled_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_il_scaled}{...}\index{bessel_il_scaled}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_il_scaled_e}{...}\index{bessel_il_scaled_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_j0}{...}\index{bessel_j0}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_j0_e}{...}\index{bessel_j0_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_j1}{...}\index{bessel_j1}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_j1_e}{...}\index{bessel_j1_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_j2}{...}\index{bessel_j2}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_j2_e}{...}\index{bessel_j2_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_jl}{...}\index{bessel_jl}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_jl_e}{...}\index{bessel_jl_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_k0_scaled}{...}\index{bessel_k0_scaled}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_k0_scaled_e}{...}\index{bessel_k0_scaled_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_k1_scaled}{...}\index{bessel_k1_scaled}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_k1_scaled_e}{...}\index{bessel_k1_scaled_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_k2_scaled}{...}\index{bessel_k2_scaled}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_k2_scaled_e}{...}\index{bessel_k2_scaled_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_kl_scaled}{...}\index{bessel_kl_scaled}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_kl_scaled_e}{...}\index{bessel_kl_scaled_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_lnKnu}{...}\index{bessel_lnKnu}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_lnKnu_e}{...}\index{bessel_lnKnu_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_y0}{...}\index{bessel_y0}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_y0_e}{...}\index{bessel_y0_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_y1}{...}\index{bessel_y1}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_y1_e}{...}\index{bessel_y1_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_y2}{...}\index{bessel_y2}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_y2_e}{...}\index{bessel_y2_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_yl}{...}\index{bessel_yl}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_yl_e}{...}\index{bessel_yl_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_zero_J0}{...}\index{bessel_zero_J0}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_zero_J0_e}{...}\index{bessel_zero_J0_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_zero_J1}{...}\index{bessel_zero_J1}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_zero_J1_e}{...}\index{bessel_zero_J1_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{bessel_zero_Jnu}{...}\index{bessel_zero_Jnu}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{bessel_zero_Jnu_e}{...}\index{bessel_zero_Jnu_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{beta}{...}\index{beta}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{beta_e}{...}\index{beta_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{beta_inc}{...}\index{beta_inc}

    Number of Input  Arguments:  3
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{beta_inc_e}{...}\index{beta_inc_e}

    Number of Input  Arguments:  3
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 3 of the C argument list

\end{funcdesc}

\begin{funcdesc}{choose}{...}\index{choose}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{choose_e}{...}\index{choose_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{clausen}{...}\index{clausen}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{clausen_e}{...}\index{clausen_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{conicalP_0}{...}\index{conicalP_0}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{conicalP_0_e}{...}\index{conicalP_0_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{conicalP_1}{...}\index{conicalP_1}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{conicalP_1_e}{...}\index{conicalP_1_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{conicalP_cyl_reg}{...}\index{conicalP_cyl_reg}

    Number of Input  Arguments:  3
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{conicalP_cyl_reg_e}{...}\index{conicalP_cyl_reg_e}

    Number of Input  Arguments:  3
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 3 of the C argument list

\end{funcdesc}

\begin{funcdesc}{conicalP_half}{...}\index{conicalP_half}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{conicalP_half_e}{...}\index{conicalP_half_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{conicalP_mhalf}{...}\index{conicalP_mhalf}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{conicalP_mhalf_e}{...}\index{conicalP_mhalf_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{conicalP_sph_reg}{...}\index{conicalP_sph_reg}

    Number of Input  Arguments:  3
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{conicalP_sph_reg_e}{...}\index{conicalP_sph_reg_e}

    Number of Input  Arguments:  3
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 3 of the C argument list

\end{funcdesc}

\begin{funcdesc}{cos}{...}\index{cos}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{cos_e}{...}\index{cos_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{cos_err_e}{...}\index{cos_err_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{coulomb_CL_e}{...}\index{coulomb_CL_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{coulomb_wave_FG_e}{...}\index{coulomb_wave_FG_e}

    Number of Input  Arguments:  4
    Number of Output Arguments: 10

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 4 of the C argument list
Return Arguments 3 and 4 resemble a gsl_result argument,
	which is  argument 5 of the C argument list
Return Arguments 5 and 6 resemble a gsl_result argument,
	which is  argument 6 of the C argument list
Return Arguments 7 and 8 resemble a gsl_result argument,
	which is  argument 7 of the C argument list

\end{funcdesc}

\begin{funcdesc}{coupling_3j}{...}\index{coupling_3j}

    Number of Input  Arguments:  6
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{coupling_3j_e}{...}\index{coupling_3j_e}

    Number of Input  Arguments:  6
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 6 of the C argument list

\end{funcdesc}

\begin{funcdesc}{coupling_6j}{...}\index{coupling_6j}

    Number of Input  Arguments:  6
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{coupling_6j_e}{...}\index{coupling_6j_e}

    Number of Input  Arguments:  6
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 6 of the C argument list

\end{funcdesc}

\begin{funcdesc}{coupling_9j}{...}\index{coupling_9j}

    Number of Input  Arguments:  9
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{coupling_9j_e}{...}\index{coupling_9j_e}

    Number of Input  Arguments:  9
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 9 of the C argument list

\end{funcdesc}

\begin{funcdesc}{coupling_RacahW}{...}\index{coupling_RacahW}

    Number of Input  Arguments:  6
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{coupling_RacahW_e}{...}\index{coupling_RacahW_e}

    Number of Input  Arguments:  6
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 6 of the C argument list

\end{funcdesc}

\begin{funcdesc}{dawson}{...}\index{dawson}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{dawson_e}{...}\index{dawson_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{debye_1}{...}\index{debye_1}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{debye_1_e}{...}\index{debye_1_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{debye_2}{...}\index{debye_2}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{debye_2_e}{...}\index{debye_2_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{debye_3}{...}\index{debye_3}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{debye_3_e}{...}\index{debye_3_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{debye_4}{...}\index{debye_4}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{debye_4_e}{...}\index{debye_4_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{dilog}{...}\index{dilog}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{dilog_e}{...}\index{dilog_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{doublefact}{...}\index{doublefact}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{doublefact_e}{...}\index{doublefact_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{ellint_D}{...}\index{ellint_D}

    Number of Input  Arguments:  4
    Number of Output Arguments:  1

 Argument 4 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX

\end{funcdesc}

\begin{funcdesc}{ellint_D_e}{...}\index{ellint_D_e}

    Number of Input  Arguments:  4
    Number of Output Arguments:  2

 Argument 4 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX
The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 4 of the C argument list

\end{funcdesc}

\begin{funcdesc}{ellint_E}{...}\index{ellint_E}

    Number of Input  Arguments:  3
    Number of Output Arguments:  1

 Argument 3 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX

\end{funcdesc}

\begin{funcdesc}{ellint_E_e}{...}\index{ellint_E_e}

    Number of Input  Arguments:  3
    Number of Output Arguments:  2

 Argument 3 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX
The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 3 of the C argument list

\end{funcdesc}

\begin{funcdesc}{ellint_Ecomp}{...}\index{ellint_Ecomp}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1

 Argument 2 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX

\end{funcdesc}

\begin{funcdesc}{ellint_Ecomp_e}{...}\index{ellint_Ecomp_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

 Argument 2 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX
The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{ellint_F}{...}\index{ellint_F}

    Number of Input  Arguments:  3
    Number of Output Arguments:  1

 Argument 3 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX

\end{funcdesc}

\begin{funcdesc}{ellint_F_e}{...}\index{ellint_F_e}

    Number of Input  Arguments:  3
    Number of Output Arguments:  2

 Argument 3 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX
The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 3 of the C argument list

\end{funcdesc}

\begin{funcdesc}{ellint_Kcomp}{...}\index{ellint_Kcomp}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1

 Argument 2 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX

\end{funcdesc}

\begin{funcdesc}{ellint_Kcomp_e}{...}\index{ellint_Kcomp_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

 Argument 2 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX
The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{ellint_P}{...}\index{ellint_P}

    Number of Input  Arguments:  4
    Number of Output Arguments:  1

 Argument 4 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX

\end{funcdesc}

\begin{funcdesc}{ellint_P_e}{...}\index{ellint_P_e}

    Number of Input  Arguments:  4
    Number of Output Arguments:  2

 Argument 4 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX
The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 4 of the C argument list

\end{funcdesc}

\begin{funcdesc}{ellint_RC}{...}\index{ellint_RC}

    Number of Input  Arguments:  3
    Number of Output Arguments:  1

 Argument 3 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX

\end{funcdesc}

\begin{funcdesc}{ellint_RC_e}{...}\index{ellint_RC_e}

    Number of Input  Arguments:  3
    Number of Output Arguments:  2

 Argument 3 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX
The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 3 of the C argument list

\end{funcdesc}

\begin{funcdesc}{ellint_RD}{...}\index{ellint_RD}

    Number of Input  Arguments:  4
    Number of Output Arguments:  1

 Argument 4 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX

\end{funcdesc}

\begin{funcdesc}{ellint_RD_e}{...}\index{ellint_RD_e}

    Number of Input  Arguments:  4
    Number of Output Arguments:  2

 Argument 4 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX
The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 4 of the C argument list

\end{funcdesc}

\begin{funcdesc}{ellint_RF}{...}\index{ellint_RF}

    Number of Input  Arguments:  4
    Number of Output Arguments:  1

 Argument 4 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX

\end{funcdesc}

\begin{funcdesc}{ellint_RF_e}{...}\index{ellint_RF_e}

    Number of Input  Arguments:  4
    Number of Output Arguments:  2

 Argument 4 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX
The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 4 of the C argument list

\end{funcdesc}

\begin{funcdesc}{ellint_RJ}{...}\index{ellint_RJ}

    Number of Input  Arguments:  5
    Number of Output Arguments:  1

 Argument 5 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX

\end{funcdesc}

\begin{funcdesc}{ellint_RJ_e}{...}\index{ellint_RJ_e}

    Number of Input  Arguments:  5
    Number of Output Arguments:  2

 Argument 5 is a gsl_mode_t, valid parameters are:
	sf.PREC_DOUBLE or sf.PREC_SINGLE or sf.PREC_APPROX
The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 5 of the C argument list

\end{funcdesc}

\begin{funcdesc}{elljac_e}{...}\index{elljac_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  3

The error flag is discarded.

\end{funcdesc}

\begin{funcdesc}{erf}{...}\index{erf}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{erf_Q}{...}\index{erf_Q}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{erf_Q_e}{...}\index{erf_Q_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{erf_Z}{...}\index{erf_Z}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{erf_Z_e}{...}\index{erf_Z_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{erf_e}{...}\index{erf_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{erfc}{...}\index{erfc}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{erfc_e}{...}\index{erfc_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{eta}{...}\index{eta}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{eta_e}{...}\index{eta_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{eta_int}{...}\index{eta_int}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{eta_int_e}{...}\index{eta_int_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{expint_3}{...}\index{expint_3}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{expint_3_e}{...}\index{expint_3_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{expint_E1}{...}\index{expint_E1}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{expint_E1_e}{...}\index{expint_E1_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{expint_E1_scaled}{...}\index{expint_E1_scaled}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{expint_E1_scaled_e}{...}\index{expint_E1_scaled_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{expint_E2}{...}\index{expint_E2}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{expint_E2_e}{...}\index{expint_E2_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{expint_E2_scaled}{...}\index{expint_E2_scaled}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{expint_E2_scaled_e}{...}\index{expint_E2_scaled_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{expint_Ei}{...}\index{expint_Ei}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{expint_Ei_e}{...}\index{expint_Ei_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{expint_Ei_scaled}{...}\index{expint_Ei_scaled}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{expint_Ei_scaled_e}{...}\index{expint_Ei_scaled_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{fact}{...}\index{fact}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{fact_e}{...}\index{fact_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{fermi_dirac_0}{...}\index{fermi_dirac_0}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{fermi_dirac_0_e}{...}\index{fermi_dirac_0_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{fermi_dirac_1}{...}\index{fermi_dirac_1}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{fermi_dirac_1_e}{...}\index{fermi_dirac_1_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{fermi_dirac_2}{...}\index{fermi_dirac_2}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{fermi_dirac_2_e}{...}\index{fermi_dirac_2_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{fermi_dirac_3half}{...}\index{fermi_dirac_3half}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{fermi_dirac_3half_e}{...}\index{fermi_dirac_3half_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{fermi_dirac_half}{...}\index{fermi_dirac_half}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{fermi_dirac_half_e}{...}\index{fermi_dirac_half_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{fermi_dirac_inc_0}{...}\index{fermi_dirac_inc_0}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{fermi_dirac_inc_0_e}{...}\index{fermi_dirac_inc_0_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{fermi_dirac_int}{...}\index{fermi_dirac_int}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{fermi_dirac_int_e}{...}\index{fermi_dirac_int_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{fermi_dirac_m1}{...}\index{fermi_dirac_m1}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{fermi_dirac_m1_e}{...}\index{fermi_dirac_m1_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{fermi_dirac_mhalf}{...}\index{fermi_dirac_mhalf}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{fermi_dirac_mhalf_e}{...}\index{fermi_dirac_mhalf_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{gamma}{...}\index{gamma}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{gamma_e}{...}\index{gamma_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{gamma_inc_P}{...}\index{gamma_inc_P}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{gamma_inc_P_e}{...}\index{gamma_inc_P_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{gamma_inc_Q}{...}\index{gamma_inc_Q}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{gamma_inc_Q_e}{...}\index{gamma_inc_Q_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{gammainv}{...}\index{gammainv}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{gammainv_e}{...}\index{gammainv_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{gammastar}{...}\index{gammastar}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{gammastar_e}{...}\index{gammastar_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{gegenpoly_1}{...}\index{gegenpoly_1}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{gegenpoly_1_e}{...}\index{gegenpoly_1_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{gegenpoly_2}{...}\index{gegenpoly_2}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{gegenpoly_2_e}{...}\index{gegenpoly_2_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{gegenpoly_3}{...}\index{gegenpoly_3}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{gegenpoly_3_e}{...}\index{gegenpoly_3_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{gegenpoly_n}{...}\index{gegenpoly_n}

    Number of Input  Arguments:  3
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{gegenpoly_n_e}{...}\index{gegenpoly_n_e}

    Number of Input  Arguments:  3
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 3 of the C argument list

\end{funcdesc}

\begin{funcdesc}{hydrogenicR}{...}\index{hydrogenicR}

    Number of Input  Arguments:  4
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{hydrogenicR_1}{...}\index{hydrogenicR_1}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{hydrogenicR_1_e}{...}\index{hydrogenicR_1_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{hydrogenicR_e}{...}\index{hydrogenicR_e}

    Number of Input  Arguments:  4
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 4 of the C argument list

\end{funcdesc}

\begin{funcdesc}{hyperg_0F1}{...}\index{hyperg_0F1}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{hyperg_0F1_e}{...}\index{hyperg_0F1_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{hyperg_1F1}{...}\index{hyperg_1F1}

    Number of Input  Arguments:  3
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{hyperg_1F1_e}{...}\index{hyperg_1F1_e}

    Number of Input  Arguments:  3
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 3 of the C argument list

\end{funcdesc}

\begin{funcdesc}{hyperg_1F1_int}{...}\index{hyperg_1F1_int}

    Number of Input  Arguments:  3
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{hyperg_1F1_int_e}{...}\index{hyperg_1F1_int_e}

    Number of Input  Arguments:  3
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 3 of the C argument list

\end{funcdesc}

\begin{funcdesc}{hyperg_2F0}{...}\index{hyperg_2F0}

    Number of Input  Arguments:  3
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{hyperg_2F0_e}{...}\index{hyperg_2F0_e}

    Number of Input  Arguments:  3
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 3 of the C argument list

\end{funcdesc}

\begin{funcdesc}{hyperg_2F1}{...}\index{hyperg_2F1}

    Number of Input  Arguments:  4
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{hyperg_2F1_conj}{...}\index{hyperg_2F1_conj}

    Number of Input  Arguments:  4
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{hyperg_2F1_conj_e}{...}\index{hyperg_2F1_conj_e}

    Number of Input  Arguments:  4
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 4 of the C argument list

\end{funcdesc}

\begin{funcdesc}{hyperg_2F1_conj_renorm}{...}\index{hyperg_2F1_conj_renorm}

    Number of Input  Arguments:  4
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{hyperg_2F1_conj_renorm_e}{...}\index{hyperg_2F1_conj_renorm_e}

    Number of Input  Arguments:  4
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 4 of the C argument list

\end{funcdesc}

\begin{funcdesc}{hyperg_2F1_e}{...}\index{hyperg_2F1_e}

    Number of Input  Arguments:  4
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 4 of the C argument list

\end{funcdesc}

\begin{funcdesc}{hyperg_2F1_renorm}{...}\index{hyperg_2F1_renorm}

    Number of Input  Arguments:  4
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{hyperg_2F1_renorm_e}{...}\index{hyperg_2F1_renorm_e}

    Number of Input  Arguments:  4
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 4 of the C argument list

\end{funcdesc}

\begin{funcdesc}{hyperg_U}{...}\index{hyperg_U}

    Number of Input  Arguments:  3
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{hyperg_U_e}{...}\index{hyperg_U_e}

    Number of Input  Arguments:  3
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 3 of the C argument list

\end{funcdesc}

\begin{funcdesc}{hyperg_U_e10_e}{...}\index{hyperg_U_e10_e}

    Number of Input  Arguments:  3
    Number of Output Arguments:  3

The error flag is discarded.
Return Arguments 1 - 3 resemble a gsl_result_e10 argument,
	which is argument 3 of the C argument list

\end{funcdesc}

\begin{funcdesc}{hyperg_U_int}{...}\index{hyperg_U_int}

    Number of Input  Arguments:  3
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{hyperg_U_int_e}{...}\index{hyperg_U_int_e}

    Number of Input  Arguments:  3
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 3 of the C argument list

\end{funcdesc}

\begin{funcdesc}{hyperg_U_int_e10_e}{...}\index{hyperg_U_int_e10_e}

    Number of Input  Arguments:  3
    Number of Output Arguments:  3

The error flag is discarded.
Return Arguments 1 - 3 resemble a gsl_result_e10 argument,
	which is argument 3 of the C argument list

\end{funcdesc}

\begin{funcdesc}{hypot}{...}\index{hypot}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{hypot_e}{...}\index{hypot_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{hzeta}{...}\index{hzeta}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{hzeta_e}{...}\index{hzeta_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{laguerre_1}{...}\index{laguerre_1}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{laguerre_1_e}{...}\index{laguerre_1_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{laguerre_2}{...}\index{laguerre_2}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{laguerre_2_e}{...}\index{laguerre_2_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{laguerre_3}{...}\index{laguerre_3}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{laguerre_3_e}{...}\index{laguerre_3_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{laguerre_n}{...}\index{laguerre_n}

    Number of Input  Arguments:  3
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{laguerre_n_e}{...}\index{laguerre_n_e}

    Number of Input  Arguments:  3
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 3 of the C argument list

\end{funcdesc}

\begin{funcdesc}{lambert_W0}{...}\index{lambert_W0}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{lambert_W0_e}{...}\index{lambert_W0_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{lambert_Wm1}{...}\index{lambert_Wm1}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{lambert_Wm1_e}{...}\index{lambert_Wm1_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{legendre_H3d}{...}\index{legendre_H3d}

    Number of Input  Arguments:  3
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{legendre_H3d_0}{...}\index{legendre_H3d_0}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{legendre_H3d_0_e}{...}\index{legendre_H3d_0_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{legendre_H3d_1}{...}\index{legendre_H3d_1}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{legendre_H3d_1_e}{...}\index{legendre_H3d_1_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{legendre_H3d_e}{...}\index{legendre_H3d_e}

    Number of Input  Arguments:  3
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 3 of the C argument list

\end{funcdesc}

\begin{funcdesc}{legendre_P1}{...}\index{legendre_P1}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{legendre_P1_e}{...}\index{legendre_P1_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{legendre_P2}{...}\index{legendre_P2}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{legendre_P2_e}{...}\index{legendre_P2_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{legendre_P3}{...}\index{legendre_P3}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{legendre_P3_e}{...}\index{legendre_P3_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{legendre_Pl}{...}\index{legendre_Pl}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{legendre_Pl_e}{...}\index{legendre_Pl_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{legendre_Plm}{...}\index{legendre_Plm}

    Number of Input  Arguments:  3
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{legendre_Plm_e}{...}\index{legendre_Plm_e}

    Number of Input  Arguments:  3
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 3 of the C argument list

\end{funcdesc}

\begin{funcdesc}{legendre_Q0}{...}\index{legendre_Q0}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{legendre_Q0_e}{...}\index{legendre_Q0_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{legendre_Q1}{...}\index{legendre_Q1}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{legendre_Q1_e}{...}\index{legendre_Q1_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{legendre_Ql}{...}\index{legendre_Ql}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{legendre_Ql_e}{...}\index{legendre_Ql_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{legendre_sphPlm}{...}\index{legendre_sphPlm}

    Number of Input  Arguments:  3
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{legendre_sphPlm_e}{...}\index{legendre_sphPlm_e}

    Number of Input  Arguments:  3
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 3 of the C argument list

\end{funcdesc}

\begin{funcdesc}{lnbeta}{...}\index{lnbeta}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{lnbeta_e}{...}\index{lnbeta_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{lnchoose}{...}\index{lnchoose}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{lnchoose_e}{...}\index{lnchoose_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{lncosh}{...}\index{lncosh}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{lncosh_e}{...}\index{lncosh_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{lndoublefact}{...}\index{lndoublefact}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{lndoublefact_e}{...}\index{lndoublefact_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{lnfact}{...}\index{lnfact}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{lnfact_e}{...}\index{lnfact_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{lngamma}{...}\index{lngamma}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{lngamma_e}{...}\index{lngamma_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{lngamma_sgn_e}{...}\index{lngamma_sgn_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  3

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{lnpoch}{...}\index{lnpoch}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{lnpoch_e}{...}\index{lnpoch_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{lnpoch_sgn_e}{...}\index{lnpoch_sgn_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  3

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{lnsinh}{...}\index{lnsinh}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{lnsinh_e}{...}\index{lnsinh_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{log}{...}\index{log}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{log_1plusx}{...}\index{log_1plusx}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{log_1plusx_e}{...}\index{log_1plusx_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{log_1plusx_mx}{...}\index{log_1plusx_mx}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{log_1plusx_mx_e}{...}\index{log_1plusx_mx_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{log_abs}{...}\index{log_abs}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{log_abs_e}{...}\index{log_abs_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{log_e}{...}\index{log_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{log_erfc}{...}\index{log_erfc}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{log_erfc_e}{...}\index{log_erfc_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{multiply}{...}\index{multiply}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{multiply_e}{...}\index{multiply_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{multiply_err_e}{...}\index{multiply_err_e}

    Number of Input  Arguments:  4
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 4 of the C argument list

\end{funcdesc}

\begin{funcdesc}{poch}{...}\index{poch}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{poch_e}{...}\index{poch_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{pochrel}{...}\index{pochrel}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{pochrel_e}{...}\index{pochrel_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{polar_to_rect}{...}\index{polar_to_rect}

\end{funcdesc}

\begin{funcdesc}{pow_int}{...}\index{pow_int}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{pow_int_e}{...}\index{pow_int_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{psi}{...}\index{psi}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{psi_1_int}{...}\index{psi_1_int}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{psi_1_int_e}{...}\index{psi_1_int_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{psi_1piy}{...}\index{psi_1piy}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{psi_1piy_e}{...}\index{psi_1piy_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{psi_e}{...}\index{psi_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{psi_int}{...}\index{psi_int}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{psi_int_e}{...}\index{psi_int_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{psi_n}{...}\index{psi_n}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{psi_n_e}{...}\index{psi_n_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{rect_to_polar}{...}\index{rect_to_polar}

\end{funcdesc}

\begin{funcdesc}{sin}{...}\index{sin}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{sin_e}{...}\index{sin_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{sin_err_e}{...}\index{sin_err_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{sinc}{...}\index{sinc}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{sinc_e}{...}\index{sinc_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{synchrotron_1}{...}\index{synchrotron_1}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{synchrotron_1_e}{...}\index{synchrotron_1_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{synchrotron_2}{...}\index{synchrotron_2}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{synchrotron_2_e}{...}\index{synchrotron_2_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{taylorcoeff}{...}\index{taylorcoeff}

    Number of Input  Arguments:  2
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{taylorcoeff_e}{...}\index{taylorcoeff_e}

    Number of Input  Arguments:  2
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 2 of the C argument list

\end{funcdesc}

\begin{funcdesc}{transport_2}{...}\index{transport_2}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{transport_2_e}{...}\index{transport_2_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{transport_3}{...}\index{transport_3}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{transport_3_e}{...}\index{transport_3_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{transport_4}{...}\index{transport_4}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{transport_4_e}{...}\index{transport_4_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{transport_5}{...}\index{transport_5}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{transport_5_e}{...}\index{transport_5_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{zeta}{...}\index{zeta}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{zeta_e}{...}\index{zeta_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\begin{funcdesc}{zeta_int}{...}\index{zeta_int}

    Number of Input  Arguments:  1
    Number of Output Arguments:  1
\end{funcdesc}

\begin{funcdesc}{zeta_int_e}{...}\index{zeta_int_e}

    Number of Input  Arguments:  1
    Number of Output Arguments:  2

The error flag is discarded.
Return Arguments 1 and 2 resemble a gsl_result argument,
	which is  argument 1 of the C argument list

\end{funcdesc}

\section{Ordinary Functions}

The following array functions have been wrapped. These are supposingly faster
than the equivalent functions from above.
\begin{funcdesc}{bessel_In_array}{...}\index{bessel_In_array}
\end{funcdesc}
\begin{funcdesc}{bessel_Jn_array}{...}\index{bessel_Jn_array}
\end{funcdesc}
\begin{funcdesc}{bessel_Kn_array}{...}\index{bessel_Kn_array}
\end{funcdesc}
\begin{funcdesc}{bessel_Kn_scaled_array}{...}\index{bessel_Kn_scaled_array}
\end{funcdesc}
\begin{funcdesc}{bessel_Yn_array}{...}\index{bessel_Yn_array}
\end{funcdesc}
\begin{funcdesc}{bessel_il_scaled_array}{...}\index{bessel_il_scaled_array}
\end{funcdesc}
\begin{funcdesc}{bessel_jl_array}{...}\index{bessel_jl_array}
\end{funcdesc}
\begin{funcdesc}{bessel_jl_steed_array}{...}\index{bessel_jl_steed_array}
\end{funcdesc}
\begin{funcdesc}{bessel_kl_scaled_array}{...}\index{bessel_kl_scaled_array}
\end{funcdesc}
\begin{funcdesc}{bessel_yl_array}{...}\index{bessel_yl_array}
\end{funcdesc}


\chapter{Introduction}
\label{sec:introduction}

The amount of information available on the internet is staggering, even conducting a simple search like \textit{St Peter's Basilica} can turn up millions of results. Fortunately, search engines ensure the first results are the most relevant and often times all we need to look at. However, this may not be true for all types of searches.

Imagine a person planning a trip to Rome for two days. Where to start? Suppose they start searching for attractions to visit or things to do. A popular site for this kind of search is \textit{tripadvisor} which shows over 2000 attractions and activities along with user reviews and recommendations, clearly it is impossible for someone to go through all these results so picking the top results and filtering for some type of activities is a good strategy. Afterwards, they must find the location of each place and organize them in a schedule and map considering travel times, visit times and locations. This certainly sounds like a complicated endeavor.

An alternative would be to find a curated itinerary that contains all the places to visit and in which order. There are many for Rome since it is such a touristic city, but what about smaller cities? Could it be possible to produce such itineraries in an automatic fashion, such that it can be scaled to multiple cities?

This is a complex problem with various questions to answer. How to obtain data about a city that is available regardless of size or popularity? How to extract meaningful information about locations and activities from such data? How to select a subset of those locations and activities that are of interest for a particular user and present it in an organized manner?

We focus on a simplified instance of this problem. Consider a user that is planning a day trip and knows some attractions to visit, however they would like to see more than that. Therefore, a method is needed that can expand the existing set of attractions to be visited in a city. This should be generated automatically from data so that it can be applied to different cities. This addresses all the questions presented before, although it excludes the problems of scheduling based on travel and visit times, which could be done as a post-processing step given a set of locations to visit.

Photos of a place are usually an important factor when selecting destinations, and it can influence the perception that a visitor has of a place. When a tourist takes a photo of some location and uploads it to the internet, they are giving it an implicit value  \citep{Donaire2014}. Several authors have used internet photo collections for the task of tourist route planning and recommendation. This is why we chose photos as the starting point for identifying popular attractions, in particular geotagged photos are of interest because they can be directly associated with a place.

One source for these photos is Flickr, a popular site where users can upload and manage their photos for free. Having over 92 million users among 63 countries makes Flickr an excellent source of photos for many locations all over the world, moreover around 1 million photos are shared every day \footnote{As reported in 2014 \url{http://techcrunch.com/2014/02/10/flickr-at-10-1m-photos-shared-per-day-170-increase-since-making-1tb-free/}}. Many of the photos in Flickr are public and available through an API which allows researchers to collect and analyze this data.

In order to model this data, we focus on probabilistic submodular models which have been used for summarization tasks and exhibit a natural capacity of modeling the concept of diversity. This work studies a submodular model known as FLID proposed by \citet{tschiatschek16learning} which was used for summarization of a large image collection and product recommendation from Amazon data, we extend it and show how this can be also applied for the problem of recommending routes for tourists. One of the extensions introduces the concept of attractiveness to the model, which aims to capture situations when it is desirable to visit multiple similar locations, for example visiting two churches on the same day. This attractiveness is achieved by incorporating supermodularity to the model. Additionally, features were introduced to show how the model can generalize to unseen elements.

The contributions of this work are:

\begin{itemize}
  \item A supermodular extension to the FLID model to integrate the concept of attractiveness.
  \item An extension to the FLID model able to generalize to unseen elements using feature representations.
  \item Exploring the behavior of noise contrastive estimation for the FLID model and its extensions, as well as the effect of different parameters in the learning results.
  \item Presenting an application of the proposed models to solve a recommendation task for touristic locations in a city.
\end{itemize}

The remainder of this document is organized as follows, Chapter \ref{sec:related_work} summarizes the existing literature and methods for the problems of summarization of image collections and tourist route recommendation based on geotagged photos, as well as literature on submodular models. Chapter \ref{sec:background} explains in detail the existing models and techniques used throughout this work. Chapter \ref{sec:models} introduces the proposed models and their characteristics, while chapter \ref{sec:synthetic} shows how they can be learned from data and the performance of the learning method. Chapter \ref{sec:experimental_setup} describes the methods used for the task of recommending tourist locations and how the proposed models were applied to real data, the results of the experiments are then presented and discussed in Chapter \ref{sec:results}. Finally, Chapter \ref{sec:conclusion} summarizes this work and presents some conclusions and future research directions.