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

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 als...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2015-08, Vol.284, p.50-57
Main Authors: Area, I., Godoy, E., Rodal, J., Ronveaux, A., Zarzo, A.
Format: Article
Language:English
Subjects:
Algorithms
Bivariate discrete orthogonal polynomials
Bivariate Krawtchouk polynomials
Byproducts
Connection problems
Generalized Appell hypergeometric series
Inversion problems
Inversions
Mathematical analysis
Mathematical models
Partial difference equations
Polynomials
Scalars
Vectors (mathematics)
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Summary: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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2014.11.022