Group-theoretic origin of some generating functions for Laguerre polynomials of two variables. (English) Zbl 1229.33020

Summary: We obtain differential equation and some recurrence relations of two-variables and one parameter Laguerre polynomials (2V1PLP). Generating relations are also obtained by means of Group theoretic method. Laguerre polynomials have special importance in engineering, sciences and constitute good model for many systems in various fields. Application of Group Theoretic Method involves the construction of a three-dimensional Lie algebra isomorphic to special linear algebra \(sl (2) \).


33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
33C50 Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable
33C80 Connections of hypergeometric functions with groups and algebras, and related topics
65Q30 Numerical aspects of recurrence relations
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