From: kovarik@mcmail.cis.mcmaster.ca (Zdislav V. Kovarik)
Subject: Re: Orthogonal polynomials
Date: 9 Feb 2001 12:27:19 -0500
Newsgroups: sci.math.research
Summary: Jacobi polynomials as an orthonormal basis in Hilbert space

In article <Pine.GSO.4.10.10102090935290.20001-100000@li.scl.cwru.edu>,
Mark W. Meckes <mwm2@po.cwru.edu> wrote:
:Is there a standard name (and perhaps a reference) for the ONB
:of L^2(0,1) one obtains by applying Gram-Schmidt to the *even*
:powers of x?
:

(Presumed: the weight in the inner product is constant 1.)
After a change of variable x^2 = t, the scalar product of
p_m(x^2), p_n(x^2) becomes

<p_m, p_n> = (1/2) * int[0 to 1] t^(-1/2) p_m(t) * p_n(t) dt

Traditional name of the simplified p_m: Jacobi polynomials
(with appropriate exponents and normalization). Handbooks 
of special functions cover them.

Cheers, ZVK(Slavek).