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Resumen de On generating functions of modified Laguerre polynomials by algebraic method

A.K. Chongdar, Giovanna Pittaluga, Laura Sacripante

  • In the present paper L.Weisner's group theoretic method of obtaining generating functions has been utilised while investigating generating functions of modified Laguerre polynomials La ,b,m,n(x) introduced by G.K .Goyal. In fact , in Section 2, by suitably interpreting the index n and the parameter m of La ,b,m,n (x) , we have introduced a set of infinitesimal operators, their commutators and the extended forro of the groups corresponding to the infinitesimal operators and on showing that they generate a seven dimensional Lie algebra, we have obtained in Section 3 a novel generating relation involving La,b,m,n(x) which as special cases yields a good number of particular generating functions most of which have not appeared in the earlier works. Furthermore, we have obtained in Section 4 ali possible variants of the main generating relation (3.3) obtained in Section 3.


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