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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Some extensions of the Mehler formula

Authors: H. M. Srivastava and J. P. Singhal
Journal: Proc. Amer. Math. Soc. 31 (1972), 135-141
MathSciNet review: 0285738
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Abstract: By using certain operational techniques, the authors prove an elegant unification of several extensions of the well-known Mehler formula for Hermite polynomials, given recently by L. Carlitz([1], [2]). It is also shown how rapidly a number of Carlitz's formulas would follow from these considerations. The last section discusses a generalization involving the product of several Hermite polynomials of different arguments.

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Keywords: Mehler's formula, operational techniques, Hermite polynomials, bilinear generating function, Rodrigues' formula, Glaisher's formula
Article copyright: © Copyright 1972 American Mathematical Society