T Amdeberhan ; Adriana Duncan ; Victor H Moll ; Vaishavi Sharma
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Filter integrals for orthogonal polynomials
hrj:8926 -
Hardy-Ramanujan Journal,
January 9, 2022,
Volume 44 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2021
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https://doi.org/10.46298/hrj.2022.8926
Filter integrals for orthogonal polynomialsArticle
Authors: T Amdeberhan 1; Adriana Duncan ; Victor H Moll ; Vaishavi Sharma
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T Amdeberhan;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.