Some definite integrals involving Jacobi polynomials

2022/01/31 by Enno Diekema, Diekema, Enno
Mathematics · Physics and Astronomy · #Mathematical functions and polynomials #Quantum Mechanics and Non-Hermitian Physics #Advanced Mathematical Identities

paper · pdf · doi:10.48550/arxiv.2201.13315

Abstract

Szmytkowski derived a certain integral with Gegenbauer polynomials. A natural generalization is to derive lookalike integrals with Jacobi polynomials. Six methods are treated to derive the first integral. The first method should be enough to prove the first integral, but by the other methods there arises remarkable formula such as par example a zero-balanced F3 Appell function which can be converted into a 2F1 hypergeometric function. Another three integrals complete the paper.

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