On the coefficients of integrated expansions and integrals of ultraspherical polynomials and their applications for solving differential equations
type: Item
instance of: scholarly article
title: On the coefficients of integrated expansions and integrals of ultraspherical polynomials and their applications for solving differential equations
zbMATH Open document ID: 0991.33003
DOI: 10.1016/S0377-0427(01)00420-4
published in: Journal of Computational and Applied Mathematics
publication date: 2002-05-21T00:00:00Z
review text: The author gives a remarkably simple proof of an analytical formula motivated by the work of \textit{T. N. Philips} and \textit{A. Karageorghis} [SIAM J. Numer. Anal. 27, No. 3, 823-830 (1990; Zbl 0701.33007)], which expresses the ultraspherical coefficients of an expansion for an infinitely differentiable function that has been integrated an arbitrary number of times in terms of the coefficients of the original expansion of the function. Another formula expressing explicitly the integrals of ultraspherical polynomials of any degree that has been integrated an arbitrary number of times of ultraspherical polynomials is also given. The tensor product of ultraspherical polynomials is used here to approximate a function of more than one variable. Formulas expressing the coefficients of differentiated expansions of double and triple ultraspherical polynomials in terms of the original expansion are then stated and proved. Some applications of how to use ultraspherical polynomials for solving ordinary and partial differential equations are also described.
Mathematics Subject Classification ID: 33C55
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 1743074
zbMATH Keywords: ultraspherical polynomials
author: E. H. Doha
reviewed by: H. M. Srivastava
MaRDI profile type: Publication
cites work: Q3661894
cites work: Q4039908
cites work: An efficient spectral method for ordinary differential equations with rational function coefficients
cites work: An accurate solution of parabolic equations by expansion in ultraspherical polynomials
cites work: The coefficients of differentiated expansions and derivatives of ultraspherical polynomials
cites work: Q4362225
cites work: Q4386989
cites work: The ultraspherical coefficients of the moments of a general-order derivative of an infinitely differentiable function
cites work: An accurate double Chebyshev spectral approximation for parabolic partial differential equations
cites work: Q5533821
cites work: Q4199478
cites work: Gegenbauer approximation and its applications to differential equations on the whole line
cites work: Chebyshev spectral methods for solving two-point boundary value problems arising in heat transfer
cites work: A note on the Chebyshev coefficients of the general order derivative of an infinitely differentiable function
cites work: On the coefficients of differentiated expansions of ultraspherical polynomials
cites work: The special functions and their approximations. Vol. I, II
cites work: On the Legendre Coefficients of a General-Order Derivative of an Infinitely Differentiable Function
cites work: On the Coefficients of Integrated Expansions of Ultraspherical Polynomials
cites work: Preconditioners for the Spectral Multigrid Method
Wikidata QID: Q127110761
description: scientific article; zbMATH DE number 1743074