On generating functions of modified Laguerre polynomials by algebraic method
- Autores: A.K. Chongdar, Giovanna Pittaluga, Laura Sacripante
- Localización: Revista de la Academia Canaria de Ciencias: = Folia Canariensis Academiae Scientiarum, ISSN 1130-4723, Vol. 8, Nº. 1, 1996, págs. 41-52
- Idioma: inglés
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Resumen
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.
