Recursion Formulas for Integrated Products of Jacobi Polynomials

authored by

Sven Beuchler, Tim Haubold, Veronika Pillwein

Abstract

From the literature it is known that orthogonal polynomials as the Jacobi polynomials can be expressed by hypergeometric series. In this paper, the authors derive several contiguous relations for terminating multivariate hypergeometric series. With these contiguous relations one can prove several recursion formulas of those series. This theoretical result allows to compute integrals over products of Jacobi polynomials in a very efficient recursive way. Moreover, the authors present an application to numerical analysis where it can be used in algorithms which compute the approximate solution of boundary value problem of partial differential equations by means of the finite elements method. With the aid of the contiguous relations, the approximate solution can be computed much faster than using numerical integration. A numerical example illustrates this effect.

Organisation(s)

Institute of Applied Mathematics
PhoenixD: Photonics, Optics, and Engineering - Innovation Across Disciplines

External Organisation(s)

Johannes Kepler University of Linz (JKU)

Type

Article

Journal

Constructive approximation

Volume

59

Pages

583-618

No. of pages

36

ISSN

0176-4276

Publication date

06.2024

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Analysis, Mathematics(all), Computational Mathematics

Electronic version(s)

https://doi.org/10.48550/arXiv.2105.08989 (Access: Open)
https://doi.org/10.1007/s00365-023-09655-z (Access: Open)