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Journal Articles Hardy-Ramanujan Journal Year : 2022

Filter integrals for orthogonal polynomials

Adriana Duncan
  • Function : Author
Victor H Moll
  • Function : Author
Vaishavi Sharma
  • Function : Author

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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hal-03498218 , version 1 (20-12-2021)

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T Amdeberhan, Adriana Duncan, Victor H Moll, Vaishavi Sharma. Filter integrals for orthogonal polynomials. Hardy-Ramanujan Journal, 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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