Bivariate second-order linear partial differential equations and orthogonal polynomial solutions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:387

Article

Area, I.²  Godoy, E.¹  Ronveaux, A.³  Zarzo, A.^4,5 

[1] Univ Vigo, Dept Matemat Aplicada 2, EE Ind, Vigo 36310, Spain

[2] Univ Vigo, Dept Matemat Aplicada 2, EE Telecomunicac, Vigo 36310, Spain

[3] Catholic Univ Louvain, Dept Math, B-1348 Louvain, Belgium

[4] Univ Granada, Fac Ciencias, Inst Carlos I Fis Teor & Computac, E-18071 Granada, Spain

[5] Univ Politecn Madrid, Dept Matemat Aplicada, ETS Ingenieros Ind, E-28040 Madrid, Spain

关键词: Second-order admissible potentially self-adjoint partial differential equations of hypergeometric type;    Bivariate orthogonal polynomials;    Rodrigues formula;    Generalized Kampe de Feriet hypergeometric series;    Appell polynomials;    Connection problems;   

DOI  :  10.1016/j.jmaa.2011.10.024

来源: Elsevier

【 摘 要 】

In this paper we construct the main algebraic and differential properties and the weight functions of orthogonal polynomial solutions of bivariate second-order linear partial differential equations, which are admissible potentially self-adjoint and of hypergeometric type. General formulae for all these properties are obtained explicitly in terms of the polynomial coefficients of the partial differential equation, using vector matrix notation. Moreover, Rodrigues representations for the polynomial eigensolutions and for their partial derivatives of any order are given. As illustration, these results are applied to a two parameter monic Appell polynomials. Finally, the non-monic case is briefly discussed. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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