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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