Extensions of the Mehler-Weisner and other results for the Hermite function

Author:
M. E. Cohen

Journal:
Math. Comp. **30** (1976), 553-564

MSC:
Primary 33A65

DOI:
https://doi.org/10.1090/S0025-5718-1976-0419894-3

MathSciNet review:
0419894

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Abstract: The purpose of this paper is to present expansions which generalize some well-known formulae for the Hermite function. Among these are the Weisner [20] extension of Mehler's [17] bilinear relation, some recent results of Carlitz [4], and the Bateman [2] addition theorem. A bilateral generating function involving the product of the Hermite and ultraspherical polynomials is given. Finally, some general polynomial expansion theorems are derived.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1976-0419894-3

Keywords:
Addition theorem,
bilinear generating function,
Gegenbauer polynomial,
generalized function,
Hermite function

Article copyright:
© Copyright 1976
American Mathematical Society