THE COEFFICIENTS OF DIFFERENTIATED EXPANSIONS OF DOUBLE AND TRIPLE JACOBI POLYNOMIALS

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Date

2012

Journal Title

Journal ISSN

Volume Title

Type

Article

Publisher

SPRINGER SINGAPORE PTE LTD

Series Info

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY;Volume: 38 Issue: 3 Pages: 739-765

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Abstract

Formulae expressing explicitly the coefficients of an expansion of double Jacobi polynomials which has been partially differentiated an arbitrary number of times with respect to its variables in terms of the coefficients of the original expansion are stated and proved. Extension to expansion of triple Jacobi polynomials is given. The results for the special cases of double and triple ultraspherical polynomials are considered. Also the results for Chebyshev polynomials of the first, second, third and fourth kinds and of Legendre polynomials are noted. An application of how to use double Jacobi polynomials for solving Poisson's equation in two variables subject to nonhomogeneous mixed boundary conditions is described.

Description

Accession Number: WOS:000315561500014

Keywords

University for Jacobi polynomials, spectral methods, hypergeometric series, Poisson's equation

Citation

Cited References in Web of Science Core Collection: 29