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### 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}.

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