THE COEFFICIENTS OF DIFFERENTIATED EXPANSIONS OF DOUBLE AND TRIPLE JACOBI POLYNOMIALS
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
Doi
Scientific Journal Rankings
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