Properties of Some of Two-Variable Orthogonal Polynomials

  • Gradimir V. MilovanovićEmail author
  • Güner Öztürk
  • Rabia Aktaş


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.


Jacobi polynomials Laguerre polynomials Generating function Bilinear generating function Bilateral generating function 

Mathematics Subject Classification

MSC 33C45 33C50 42C05 



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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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019

Authors and Affiliations

  1. 1.Serbian Academy of Sciences and ArtsBeogradSerbia
  2. 2.Faculty of Science and MathematicsUniversity of NišNišSerbia
  3. 3.Department of Mathematics, Faculty of ScienceSelçuk UniversitySelcuklu, KonyaTurkey
  4. 4.Department of Mathematics, Faculty of ScienceAnkara UniversityTandoğan, AnkaraTurkey

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