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On a Family of 2-Variable Orthogonal Krawtchouk Polynomials

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arxiv 1007.4327 v3 pith:63AJK6X5 submitted 2010-07-25 math.CA math.CO

F. Alberto Grünbaum , Mizan Rahman This is my paper · ORCID
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keywords polynomialsfamilykrawtchoukorthogonalityprobabilityproofvariableangular
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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.

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  1. Exactly solvable multicomponent spinless fermions

    hep-th 2025-02 conditional novelty 5.0 of 10

    Four exactly solvable multicomponent spinless fermion models are constructed from multivariate Krawtchouk, Meixner, and two Rahman-like polynomial families.

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