Gegenbauer Polynomials and Related Functions

Functions to compute Gegenbauer polynomials, their derivatives, and related functions.

Usage

gegenbauer(n, lambda, x)

gegenbauer_prime(n, lambda, x)

gegenbauer_derivative(n, lambda, x, k)

Arguments

n

Degree of the polynomial

lambda

Parameter of the polynomial

x

Argument of the polynomial

k

Order of the derivative

Value

A single numeric value with the computed Gegenbauer polynomial, its derivative, or k-th derivative.

See also

Boost Documentation for more details on the mathematical background.

Examples

# Gegenbauer polynomial C_2^(1)(0.5)
gegenbauer(2, 1, 0.5)
#> [1] 0
# Derivative of the Gegenbauer polynomial C_2^(1)'(0.5)
gegenbauer_prime(2, 1, 0.5)
#> [1] 4
# k-th derivative of the Gegenbauer polynomial C_2^(1)''(0.5)
gegenbauer_derivative(2, 1, 0.5, 2)
#> [1] 8