Bivariate Krawtchouk polynomials: Inversion and connection problems with the NAVIMA algorithm

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:284

Article

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

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

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

[3] Catholic Univ Louvain, Inst Rech Math & Phys, B-1348 Louvain La Neuve, Belgium

[4] Univ Politecn Madrid, ETS Ingn Ind, Dept Matemat Aplicada, E-28040 Madrid, Spain

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

关键词: Bivariate discrete orthogonal polynomials;    Bivariate Krawtchouk polynomials;    Inversion problems;    Connection problems;    Partial difference equations;    Generalized Appell hypergeometric series;   

DOI  :  10.1016/j.cam.2014.11.022

来源: Elsevier

【 摘 要 】

In this paper we present a recurrent procedure to solve an inversion problem for monic bivariate Krawtchouk polynomials written in vector column form, giving its solution explicitly. As a by-product, a general connection problem between two vector column of monic bivariate Krawtchouk families is also explicitly solved. Moreover, in the non monic case and also for Krawtchouk families, several expansion formulas are given, but for polynomials written in scalar form. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free