orthopolynom (version 1.0-2)

ghermite.h.polynomials: Create list of generalized Hermite polynomials

Description

This function returns a list with $n$+1 elements containing the order $k$ generalized Hermite polynomials, $H_k^{\left( \mu \right)} \left( x \right)$, 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

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

Details

The parameter $\mu$ must be greater than -0.5.

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 )