English

Filter integrals for orthogonal polynomials

Classical Analysis and ODEs 2020-12-16 v2

Abstract

Motivated by an expression by Persson and Strang on an integral involving Legendre polynomials, stating that the square of P2n+1(x)/xP_{2n+1}(x)/x integrated over [1,1][-1,1] is always 22, we present analog results for Hermite, Chebyshev, Laguerre and Gegenbauer polynomials as well as the original Legendre polynomial with even index.

Keywords

Cite

@article{arxiv.2012.05040,
  title  = {Filter integrals for orthogonal polynomials},
  author = {Tewodros Amdeberhan and Adriana Duncan and Victor H. Moll and Vaishavi Sharma},
  journal= {arXiv preprint arXiv:2012.05040},
  year   = {2020}
}
R2 v1 2026-06-23T20:50:39.726Z