legendre_polynomials: Legendre Polynomials and Related Functions

In boostmath: 'R' Bindings for the 'Boost' Math Functions

Legendre Polynomials and Related Functions

Description

Functions to compute Legendre polynomials of the first and second kind, their derivatives, zeros, and related functions.

Usage

legendre_p(n, x)

legendre_p_prime(n, x)

legendre_p_zeros(n)

legendre_p_m(n, m, x)

legendre_q(n, x)

legendre_next(n, x, Pl, Plm1)

legendre_next_m(n, m, x, Pl, Plm1)

Arguments

n	Degree of the polynomial
x	Argument of the polynomial
m	Order of the polynomial (for Legendre polynomials of the first kind)
Pl	Value of the Legendre polynomial (P_l(x))
Plm1	Value of the Legendre polynomial (P_{l-1}(x))

Value

A single numeric value with the computed Legendre polynomial, its derivative, zeros, or related functions.

See Also

Boost Documentation for more details on the mathematical background.

Examples

# Legendre polynomial of the first kind P_2(0.5)
legendre_p(2, 0.5)
# Derivative of the Legendre polynomial of the first kind P_2'(0.5)
legendre_p_prime(2, 0.5)
# Zeros of the Legendre polynomial of the first kind P_2
legendre_p_zeros(2)
# Legendre polynomial of the first kind with order 1 P_2^1(0.5)
legendre_p_m(2, 1, 0.5)
# Legendre polynomial of the second kind Q_2(0.5)
legendre_q(2, 0.5)
# Next Legendre polynomial of the first kind P_3(0.5) using P_2(0.5) and P_1(0.5)
legendre_next(2, 0.5, legendre_p(2, 0.5), legendre_p(1, 0.5))
# Next Legendre polynomial of the first kind with order 1 P_3^1(0.5) using P_2^1(0.5) and P_1^1(0.5)
legendre_next_m(2, 1, 0.5, legendre_p_m(2, 1, 0.5), legendre_p_m(1, 1, 0.5))

boostmath documentation built on Dec. 15, 2025, 5:07 p.m.