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Properties of Some of Two-Variable Orthogonal Polynomials

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Abstract

The present paper deals with various recurrence relations, generating functions and series expansion formulas for two families of orthogonal polynomials in two variables, given Laguerre–Laguerre Koornwinder polynomials and Laguerre–Jacobi Koornwinder polynomials in the limit cases. Several families of bilinear and bilateral generating functions are derived. Furthermore, some special cases of the results presented in this study are indicated.

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Acknowledgements

The authors are deeply grateful to the anonymous referees for their comments and constructive suggestions for improvements of this paper. The first author was supported in part by the Serbian Academy of Sciences and Arts (No. \(\Phi \)-96) and by the Serbian Ministry of Education, Science and Technological Development (No. #OI 174015).

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Authors and Affiliations

  1. Serbian Academy of Sciences and Arts, Kneza Mihaila 35, Beograd, 11000, Serbia

    Gradimir V. Milovanović

  2. Faculty of Science and Mathematics, University of Niš, Niš, 18000, Serbia

    Gradimir V. Milovanović

  3. Department of Mathematics, Faculty of Science, Selçuk University, 42003, Selcuklu, Konya, Turkey

    Güner Öztürk

  4. Department of Mathematics, Faculty of Science, Ankara University, 06100, Tandoğan, Ankara, Turkey

    Rabia Aktaş

Authors
  1. Gradimir V. Milovanović
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  2. Güner Öztürk
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  3. Rabia Aktaş
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Correspondence to Gradimir V. Milovanović.

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Communicated by Ali Hassan Mohamed Murid.

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Milovanović, G.V., Öztürk, G. & Aktaş, R. Properties of Some of Two-Variable Orthogonal Polynomials. Bull. Malays. Math. Sci. Soc. 43, 1403–1431 (2020). https://doi.org/10.1007/s40840-019-00750-8

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  • DOI: https://doi.org/10.1007/s40840-019-00750-8

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