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\Large \textbf{\noindent
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Divided-difference equation and three-term recurrence relations  of some systems of bivariate $q$-orthogonal polynomials}
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 \underline{D.D.~Tcheutia}$^1$,  M.~Foupouagnigni$^2$,  I.~Area$^3$,  E.~Godoy$^4$,  Y.~Guemo  Teffo$^5$
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$^1$ University of Kassel,
duvtcheutia@yahoo.fr\\
$^2$ African Institute for Mathematical Sciences, Limb\'{e}, Cameroon,
foupouagnigni@gmail.com\\
$^3$ Departamento de Matem\'atica Aplicada II, E.E. Telecomunicaci\'on, Universidade de Vigo, Campus Lagoas-Marcosende, 36310 Vigo, Spain,
area@uvigo.es\\
$^4$ Departamento de Matem\'atica Aplicada II,  E.E. Industrial, Universidade de Vigo, Campus Lagoas-Marcosende,   36310 Vigo, Spain,
egodoy@dma.uvigo.es\\
$^5$ University of Yaound\'{e} I,
guemoyves2000@yahoo.fr\\
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In this work,  partial divided-difference equations and three-term recurrence relations satisfied by the bivariate Askey-Wilson and the  bivariate $q$-Racah polynomials are computed.  By using limiting processes,  partial divided-difference equations and three-term recurrence relations   are also provided for each of the following families of orthogonal polynomials:  the bivariate continuous dual $q$-Hahn, the bivariate Al-Salam-Chihara, the bivariate continuous $q$-Hahn, the bivariate $q$-Hahn, the bivariate dual $q$-Hahn, the bivariate $q$-Krawtchouk, the bivariate $q$-Meixner, and the bivariate $q$-Charlier polynomials. We obtain our results which are all new using mainly the  \texttt{qsimpcomb} algorithm implemented in Maple in the package \texttt{qsum.mpl}.
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%\bibitem{KR} B. Keller and I. Reiten, \textit{Cluster-titled algebras are Gorenstein and stably Calabi-Yau}, Adv. Math. \textbf{211}, 1, pp. 123-151 (2007).
%\bibitem{WK} S. Washito and K. Karabashi, \textit{Use This Template}, in \textit{Proceedings of the 5th
%International Conference on Photon Interaction} (ICPI-2012), San Francisco, USA, ed. A. Chen, pp. 22-24 (2012).
%\bibitem{ABS} A.B. Smith, \textit{Describing the style for the AMMCS-CAIMS-2015 book of abstracts}, in C.D. Science (ed.), General Book of Wisdom, 2\textsuperscript{nd} ed., University of Queensland, pp. 23-42 (2011).
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