Two-variable orthogonal polynomials of big q-Jacobi type |
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Authors: | Stanis?aw Lewanowicz |
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Affiliation: | Institute of Computer Science, University of Wroc?aw, ul. Joliot-Curie 15, 50-383 Wroc?aw, Poland |
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Abstract: | A four-parameter family of orthogonal polynomials in two discrete variables is defined for a weight function of basic hypergeometric type. The polynomials, which are expressed in terms of univariate big q-Jacobi polynomials, form an extension of Dunkl’s bivariate (little) q-Jacobi polynomials [C.F. Dunkl, Orthogonal polynomials in two variables of q-Hahn and q-Jacobi type, SIAM J. Algebr. Discrete Methods 1 (1980) 137-151]. We prove orthogonality property of the new polynomials, and show that they satisfy a three-term relation in a vector-matrix notation, as well as a second-order partial q-difference equation. |
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Keywords: | 33D50 33C50 |
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