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Mathematics of Computation

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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
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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Keywords: Generating functions, Hermite polynomial, hypergeometric function, incomplete gamma function, Laguerre polynomial, operators
Article copyright: © Copyright 1977 American Mathematical Society