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 polynomialsArticle

Authors: T Amdeberhan 1; Adriana Duncan ; Victor H Moll ; Vaishavi Sharma

  • 1 Department of Mathematics [Tulane, New Orleans]

Motivated by an expression by Persson and Strang on an integral involving Legendre polynomials, stating that the square of P2n+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]

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