Legendre Polynomials

Function: double gsl_sf_legendre_P1 (double x)

Function: double gsl_sf_legendre_P2 (double x)

Function: double gsl_sf_legendre_P3 (double x)

Function: int gsl_sf_legendre_P1_e (double x, gsl_sf_result * result)

Function: int gsl_sf_legendre_P2_e (double x, gsl_sf_result * result)

Function: int gsl_sf_legendre_P3_e (double x, gsl_sf_result * result)

These functions evaluate the Legendre polynomials @math{P_l(x)} using explicit representations for @math{l=1, 2, 3}.

Function: double gsl_sf_legendre_Pl (int l, double x)

Function: int gsl_sf_legendre_Pl_e (int l, double x, gsl_sf_result * result)

These functions evaluate the Legendre polynomial @c{$P_l(x)$} @math{P_l(x)} for a specific value of l, x subject to @c{$l \ge 0$} @math{l >= 0}, @math{|x| <= 1}

Function: int gsl_sf_legendre_Pl_array (int lmax, double x, double result_array[])

This function computes an array of Legendre polynomials @math{P_l(x)} for @math{l = 0, \dots, lmax}, @math{|x| <= 1}

Function: double gsl_sf_legendre_Q0 (double x)

Function: int gsl_sf_legendre_Q0_e (double x, gsl_sf_result * result)

These routines compute the Legendre function @math{Q_0(x)} for @math{x > -1}, @c{$x \ne 1$} @math{x != 1}.

Function: double gsl_sf_legendre_Q1 (double x)

Function: int gsl_sf_legendre_Q1_e (double x, gsl_sf_result * result)

These routines compute the Legendre function @math{Q_1(x)} for @math{x > -1}, @c{$x \ne 1$} @math{x != 1}.

Function: double gsl_sf_legendre_Ql (int l, double x)

Function: int gsl_sf_legendre_Ql_e (int l, double x, gsl_sf_result * result)

These routines compute the Legendre function @math{Q_l(x)} for @math{x > -1}, @c{$x \ne 1$} @math{x != 1} and @c{$l \ge 0$} @math{l >= 0}.