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The Integral Representation for the Product of Two Parabolic Cylinder Functions $D_ν(x) D_ν(-x)$ at $Re ν<0$ by Means of the Fundamental Solution of a Landau-Type Operator

C. Malyshev
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Abstract

The fundamental solution (Green's function) of a first order matrix ordinary differential equation arising in a Landau-type problem is calculated by two methods. The coincidence of the two representations results in the integral formula for the product of two parabolic cylinder functions $D_ν(x) D_ν(-x)$ at $Re ν<0$, $x$ is real.

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C. Malyshev. 2001-12-04. The Integral Representation for the Product of Two Parabolic Cylinder Functions $D_ν(x) D_ν(-x)$ at $Re ν<0$ by Means of the Fundamental Solution of a Landau-Type Operator. https://doi.org/10.1080/1065246031000074371

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