orthopolynom (version 1.0-2)

ghermite.h.inner.products: Inner products of generalized Hermite polynomials

Description

This function returns a vector with $n$+1 elements containing the inner product of an order $k$ generalized Hermite polynomial, $H_k^{\left( \mu \right)} \left( x \right)$, with itself (i.e. the norm squared) for orders $k$ = 0, 1, ... , $n$.

Usage

ghermite.h.inner.products(n, mu)

Arguments

n

n integer highest polynomial order

mu

mu polynomial parameter

Value

• A vector with $n$+1 elements
• 1
  inner product of order 0 orthogonal polynomial
• 2
  inner product of order 1 orthogonal polynomial
• ...
• n+1
  inner product of order $n$+1 orthogonal polynomial

Details

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

References

Abramowitz and Stegun (1968)

Examples

h <- ghermite.h.inner.products( 10, 1 )