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# Filter integrals for orthogonal polynomials

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-03498218
Contributor : Srinivas Kotyada Connect in order to contact the contributor
Submitted on : Monday, December 20, 2021 - 10:30:24 PM
Last modification on : Monday, March 28, 2022 - 8:14:08 AM

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44Article10.pdf
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### Citation

T Amdeberhan, Adriana Duncan, Victor H Moll, Vaishavi Sharma. Filter integrals for orthogonal polynomials. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2022, Special Commemorative volume in honour of Srinivasa Ramanujan - 2021, Volume 44 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2021, pp.116 -- 135. ⟨10.46298/hrj.2022.8926⟩. ⟨hal-03498218⟩

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