Some classes of generating functions for the Laguerre and Hermite polynomials

Author:
M. E. Cohen

Journal:
Math. Comp. **31** (1977), 511-518

MSC:
Primary 33A65

DOI:
https://doi.org/10.1090/S0025-5718-1977-0442323-1

MathSciNet review:
0442323

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Abstract: In the first half of the article, we present two theorems which give, as special cases, a number of new classes of generating functions for the Laguerre polynomial. These formulae extend the recent results of Carlitz [2] and others. The latter part of our work deals with two theorems involving new generating functions for the Hermite and generalized Hermite polynomials, thus generalizing some well-known expansions. The method of proof adopted in this paper differs from that of previous workers.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1977-0442323-1

Keywords:
Generating functions,
Hermite polynomial,
hypergeometric function,
incomplete gamma function,
Laguerre polynomial,
operators

Article copyright:
© Copyright 1977
American Mathematical Society