## T Amdeberhan ; Adriana Duncan ; Victor H Moll ; Vaishavi Sharma - Filter integrals for orthogonal polynomials

hrj:8926 - Hardy-Ramanujan Journal, January 9, 2022, Volume 44 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2021 - https://doi.org/10.46298/hrj.2022.8926
Filter integrals for orthogonal polynomials

Authors: T Amdeberhan ; Adriana Duncan ; Victor H Moll ; Vaishavi Sharma

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

Volume: Volume 44 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2021
Published on: January 9, 2022
Accepted on: January 9, 2022
Submitted on: January 6, 2022
Keywords: Integrals,Legendre polynomials,Hermite polynomials,Chebyshev polynomials,Laguerre polynomials,Gegenbauer polynomials,2010 Mathematics Subject Classification. Primary 33C45; Secondary 33E20,[MATH]Mathematics [math]