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GNU Scientific Library Reference Manual - Third Edition (v1.12)
by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. Rossi
Paperback (6"x9"), 592 pages, 60 figures
ISBN 0954612078
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7.24.1 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 P_l(x) using explicit representations for 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 P_l(x) for a specific value of l, x subject to l >= 0, |x| <= 1
Function: int gsl_sf_legendre_Pl_array (int lmax, double x, double result_array[])
Function: int gsl_sf_legendre_Pl_deriv_array (int lmax, double x, double result_array[], double result_deriv_array[])
These functions compute an array of Legendre polynomials P_l(x), and optionally their derivatives dP_l(x)/dx, for l = 0, \dots, lmax, |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 Q_0(x) for x > -1, 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 Q_1(x) for x > -1, 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 Q_l(x) for x > -1, x != 1 and l >= 0.
ISBN 0954612078GNU Scientific Library Reference Manual - Third Edition (v1.12)See the print edition