An integral representation for the product of two parabolic cylinder functions having unrelated arguments

preprint2015arXivOpen access

An integral representation is provided for the parabolic cylinder function product $D_μ(x)D_μ(-y)$ where $Re\,μ<0$ and $x>y$ are unrelated. A few simple consequences are given in the form of hyperbolic integrals and a sum rule.

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An integral representation for the product of two parabolic cylinder functions having unrelated arguments

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