ghermite.h.polynomials {orthopolynom}R Documentation

Create list of generalized Hermite polynomials

Description

This function returns a list with $n$+1 elements containing the order $k$ generalized Hermite polynomials, H_k^{( μ )} ( x ), for orders $k$ = 0, 1, ..., $n$.

Usage

ghermite.h.polynomials(n, mu, normalized = FALSE)

Arguments

n n integer highest polynomial order
mu mu polynomial parameter
normalized normalized boolean value which, if TRUE, returns recurrence relations for normalized polynomials

Details

The parameter μ must be greater than -0.5.

Value

A list of $n$+1 polynomial objects

1 order 0 generalized Hermite polynomial
2 order 1 generalized Hermite polynomial
n+1 order $n$ generalized Hermite polynomial

Author(s)

Frederick Novomestky fnovomes@poly.edu

References

Alvarez-Nordase, Atakishiyeva, Atakishiyeva (2004)

See Also

ghermite.h.recurrences, orthogonal.polynomials, orthonormal.polynomials

Examples

normalized.p.list <- ghermite.h.polynomials( 10, 1, normalized=TRUE )
unnormalized.p.list <- ghermite.h.polynomials( 10, 1, normalized=FALSE )

[Package orthopolynom version 1.0-1 Index]