Recursion Formulas for Integrated Products of Jacobi Polynomials

verfasst von

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.

Organisationseinheit(en)

Institut für Angewandte Mathematik
PhoenixD: Simulation, Fabrikation und Anwendung optischer Systeme

Externe Organisation(en)

Johannes Kepler Universität Linz (JKU)

Typ

Artikel

Journal

Constructive approximation

ISSN

0176-4276

Publikationsdatum

27.05.2023

Publikationsstatus

Elektronisch veröffentlicht (E-Pub)

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Analysis, Mathematik (insg.), Computational Mathematics

Elektronische Version(en)

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