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arXiv · 1411.7299

Two-variable $-1$ Jacobi polynomials

Vincent X. Genest·Jean-Michel Lemay·Luc Vinet·Alexei Zhedanov
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Abstract

A two-variable generalization of the Big $-1$ Jacobi polynomials is introduced and characterized. These bivariate polynomials are constructed as a coupled product of two univariate Big $-1$ Jacobi polynomials. Their orthogonality measure is obtained. Their bispectral properties (eigenvalue equations and recurrence relations) are determined through a limiting process from the two-variable Big $q$-Jacobi polynomials of Lewanowicz and Wo\'zny. An alternative derivation of the weight function using Pearson-type equations is presented.

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Vincent X. Genest, Jean-Michel Lemay, Luc Vinet, Alexei Zhedanov. 2014-11-26. Two-variable $-1$ Jacobi polynomials. https://arxiv.org/abs/1411.7299

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