Abstract
In this paper, we analyze second-order linear partial difference equations having bivariate symmetric orthogonal polynomial solutions. We present conditions to have admissible, potentially self-adjoint partial difference equations of hypergeometric type having orthogonal polynomial solutions. For these solutions, we give explicitly the matrix coefficients of the three-term recurrence relations they satisfy. Finally, conditions in order to have symmetric orthogonal polynomial solutions are presented.
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Acknowledgements
Y. Guemo Tefo and I. Area thank the hospitality of the African Institute for Mathematical Sciences (AIMS-Cameroon), where a significant part of this research was performed during their visits in November 2014, and May and June 2015. The work of I. Area has been partially supported by the Agencia Estatal de Innovacioón (AEI) of Spain under grant MTM2016-75140-P, co-financed by the European Community fund FEDER, and Xunta de Galicia, grants GRC 2015-004 and R 2016/022.
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Guemo Tefo, Y., Area, I., Foupouagnigni, M. (2017). Bivariate Symmetric Discrete Orthogonal Polynomials. In: Ruzhansky, M., Cho, Y., Agarwal, P., Area, I. (eds) Advances in Real and Complex Analysis with Applications. Trends in Mathematics. Birkhäuser, Singapore. https://doi.org/10.1007/978-981-10-4337-6_5
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DOI: https://doi.org/10.1007/978-981-10-4337-6_5
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