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 , Mark W. Meckes 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 = (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).