Properties of Some of Two-Variable Orthogonal Polynomials
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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.
KeywordsJacobi polynomials Laguerre polynomials Generating function Bilinear generating function Bilateral generating function
Mathematics Subject ClassificationMSC 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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