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

Details 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 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

2001-06-17

arxiv.org/abs/math/0106142v2

Integral Transforms and Special Functions, Vol.14, No.2 (2003), 139-148

Mathematics

Classical Analysis and ODEs

13 pages, LaTeX, notes added

Scientific paper

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 $D_\nu(x)
D_\nu(-x)$ at $Re \nu <0$, $x$ is real.

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