A generalization of a result on generating functions of modified Laguerre polynomial by using the notion of partial quasibilinear generating function
DOI:
https://doi.org/10.5269/bspm.63347Resumen
In his paper [2], Chongdar obtained an extension (Theorem 3) of the result on bilateral generating functions involving modified Laguerre polynomial stated in Theorem 1 of Ghosh [3]. In this article, the present authors have made an attempt to present a further generalization of the extension obtained by Chongdar [2] by means of the theory of one parameter group of continuous transformations as well as using the concepts of partial quasibilateral generating function [4] involving some special functions.
Referencias
1. Chatterjea S. K. and Chakraborty S. P., A unified group-theoretic method of obtaing a more general class of generating relations from a given class of quasi bilateral (or quasi bilinear) generating relations involving some special functions, Pure Math. Manuscript 8, 153–162, (1989).
2. Chongdar, A. K., On a class of bilateral generating functions for certain special functions, Proceedings of the Indian Academy of Sciences-Mathematical Sciences 95, 133-140, (1986).
3. Ghosh, B., Some theorems on generating functions of modified Laguerre Polynomials, Bull. Cal. Math. Soc. 79, 41-47, (1987).
4. Mondal, A. K., A unified group-theoretic method of obtaining a more general class of generating relations from a given class of partial quasi-bilateral (or partial quasi-bilinear) generating relations involving some special functions, Pure Math. Manuscript 10, 121-132, (1992-93).
5. Mondal, A. K., Partial quasi-bilateral generating function involving Laguerre and Gegenbauer polynomials (I), Pure Math. Manuscript 10, 97-103, (1992-93).
6. Mondal, A. K., Partial quasi-bilinear generating function involving Laguerre polynomials, Pure Math. Manuscript 10, 89-95, (1993).
7. Weisner, L., Group - theoretic origin of certain generating functions, Pacific J. Math. 5, 1033–1039, (1955).
8. Weisner, L., Generating functions for Hermite functions, Canad. J. Math. 11, 141–147, (1959).
9. Weisner, L., Generating functions for Bessel functions, Canad. J. Math. 11, 148–155, (1959).
2. Chongdar, A. K., On a class of bilateral generating functions for certain special functions, Proceedings of the Indian Academy of Sciences-Mathematical Sciences 95, 133-140, (1986).
3. Ghosh, B., Some theorems on generating functions of modified Laguerre Polynomials, Bull. Cal. Math. Soc. 79, 41-47, (1987).
4. Mondal, A. K., A unified group-theoretic method of obtaining a more general class of generating relations from a given class of partial quasi-bilateral (or partial quasi-bilinear) generating relations involving some special functions, Pure Math. Manuscript 10, 121-132, (1992-93).
5. Mondal, A. K., Partial quasi-bilateral generating function involving Laguerre and Gegenbauer polynomials (I), Pure Math. Manuscript 10, 97-103, (1992-93).
6. Mondal, A. K., Partial quasi-bilinear generating function involving Laguerre polynomials, Pure Math. Manuscript 10, 89-95, (1993).
7. Weisner, L., Group - theoretic origin of certain generating functions, Pacific J. Math. 5, 1033–1039, (1955).
8. Weisner, L., Generating functions for Hermite functions, Canad. J. Math. 11, 141–147, (1959).
9. Weisner, L., Generating functions for Bessel functions, Canad. J. Math. 11, 148–155, (1959).
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2024-04-26
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