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arXiv:1503.06290 [math.CA]AbstractReferencesReviewsResources

Nicholson-type integrals for products of parabolic cylinder functions involving Laplace transform of confluent hypergeometric functions

Ridha Nasri

Published 2015-03-21Version 1

In this paper, we establish new formulas for the product of parabolic cylinder functions with different parameters. These formulas entail the Laplace transform of Kummer's confluent hypergeometric functions. We show then that these new identities yield Nicholson-type integrals for the product of two parabolic cylinder functions generalizing thus some known ones. Besides, we use the new integral representations to derive other series expansions for products of parabolic cylinder functions.

Comments: Preprint submitted to Journal of Mathematical Analysis and Applications. Submitted December 17, 2014
Categories: math.CA, math.CV
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