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Laguerre Polynomials and Related Functions

Source: R/polynomials.R
laguerre_polynomials.Rd

Functions to compute Laguerre polynomials of the first kind.

Usage

laguerre(n, x)

laguerre_m(n, m, x)

laguerre_next(n, x, Ln, Lnm1)

laguerre_next_m(n, m, x, Ln, Lnm1)

Arguments

n

Degree of the polynomial

x

Argument of the polynomial

m

Order of the polynomial (for Laguerre polynomials of the first kind)

Ln

Value of the Laguerre polynomial \((L_n(x))\)

Lnm1

Value of the Laguerre polynomial \((L_{n-1}(x))\)

Value

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

See also

Boost Documentation for more details on the mathematical background.

Examples

# Laguerre polynomial of the first kind L_2(0.5)
laguerre(2, 0.5)
#> [1] 0.125
# Laguerre polynomial of the first kind with order 1 L_2^1(0.5)
laguerre_m(2, 1, 0.5)
#> [1] 1.625
# Next Laguerre polynomial of the first kind L_3(0.5) using L_2(0.5) and L_1(0.5)
laguerre_next(2, 0.5, laguerre(2, 0.5), laguerre(1, 0.5))
#> [1] -0.1458333
# Next Laguerre polynomial of the first kind with order 1 L_3^1(0.5) using L_2^1(0.5) and L_1^1(0.5)
laguerre_next_m(2, 1, 0.5, laguerre_m(2, 1, 0.5), laguerre_m(1, 1, 0.5))
#> [1] 1.479167