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Symmetry, Integrability and Geometry: Methods and Applications, 2010, Volume 6, 090, 12 pp.
DOI: https://doi.org/10.3842/SIGMA.2010.090 (Mi sigma548) 		 
This article is cited in 13 scientific papers (total in 13 papers)

On a Family of $2$-Variable Orthogonal Krawtchouk Polynomials

F. Alberto Grünbauma, Mizan Rahmanb

a Department of Mathematics, University of California, Berkeley, CA 94720, USA
b Department of Mathematics and Statistics, Carleton University, Ottawa, Canada, K1S 5B6
Full-text PDF (233 kB) Citations (13)
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DOI: https://doi.org/10.3842/SIGMA.2010.090
Abstract: We give a hypergeometric proof involving a family of $2$-variable Krawtchouk polynomials that were obtained earlier by Hoare and Rahman [SIGMA 4 (2008), 089, 18 pages] as a limit of the $9-j$ symbols of quantum angular momentum theory, and shown to be eigenfunctions of the transition probability kernel corresponding to a “poker dice” type probability model. The proof in this paper derives and makes use of the necessary and sufficient conditions of orthogonality in establishing orthogonality as well as indicating their geometrical significance. We also derive a $5$-term recurrence relation satisfied by these polynomials.
Keywords: hypergeometric functions; Krawtchouk polynomials in $1$ and $2$ variables; Appell–Kampe–de Feriet functions; integral representations; transition probability kernels; recurrence relations.
Received: July 25, 2010; in final form December 1, 2010; Published online December 7, 2010
Bibliographic databases:
Document Type: Article
MSC: 33C45
Language: English
Citation: F. Alberto Grünbaum, Mizan Rahman, “On a Family of $2$-Variable Orthogonal Krawtchouk Polynomials”, SIGMA, 6 (2010), 090, 12 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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