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
NULL##NULL##NULL##NULL
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 $P_{2n+1}(x)/x$ 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.