Jacobi Polynomials and Related Functions

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

Usage

jacobi(n, alpha, beta, x)

jacobi_prime(n, alpha, beta, x)

jacobi_double_prime(n, alpha, beta, x)

jacobi_derivative(n, alpha, beta, x, k)

Arguments

n

Degree of the polynomial

alpha

First parameter of the polynomial

beta

Second parameter of the polynomial

x

Argument of the polynomial

k

Order of the derivative

Value

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

See also

Boost Documentation for more details on the mathematical background.

Examples

# Jacobi polynomial P_2^(1, 2)(0.5)
jacobi(2, 1, 2, 0.5)
#> [1] -0.1875
# Derivative of the Jacobi polynomial P_2^(1, 2)'(0.5)
jacobi_prime(2, 1, 2, 0.5)
#> [1] 3.75
# Second derivative of the Jacobi polynomial P_2^(1, 2)''(0.5)
jacobi_double_prime(2, 1, 2, 0.5)
#> [1] 10.5
# 3rd derivative of the Jacobi polynomial P_2^(1, 2)^(k)(0.5)
jacobi_derivative(2, 1, 2, 0.5, 3)
#> [1] 0