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 $P_{2n+1}(x)/x$ 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: 2010 Mathematics Subject Classification. Primary 33C45; Secondary 33E20, [MATH]Mathematics [math], [en] Integrals, Legendre polynomials, Hermite polynomials, Chebyshev polynomials, Laguerre polynomials, Gegenbauer polynomials