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Product of parabolic cylinder functions involving Laplace transforms of confluent hypergeometric functions (1503.06290v2)

Published 21 Mar 2015 in math.CA and math.CV

Abstract: In this paper, the product of parabolic cylinder functions $D_{\nu}(\pm z)D_{\nu+\mu-1}(z)$, with different parameters $\mu$ and $\nu$, 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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