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arXiv · 1503.06290

Product of parabolic cylinder functions involving Laplace transforms of confluent hypergeometric functions

Ridha Nasri
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Abstract

In this paper, the product of parabolic cylinder functions $D_ν(\pm z)D_{ν+μ-1}(z)$, with different parameters $μ$ and $ν$, are established in terms of Laplace and Fourier transforms of Kummer's confluent hypergeometric functions. The provided integral representations are transformed to easily yield Nicholson-type integral forms and used to derive other series expansions for products of parabolic cylinder functions.

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Ridha Nasri. 2016-02-24. Product of parabolic cylinder functions involving Laplace transforms of confluent hypergeometric functions. https://doi.org/10.1080/10652469.2015.1110700

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