The Integral Representation for the Product of Two Parabolic Cylinder Functions Dν(x) Dν(-x) at Re ν<0 by Means of the Fundamental Solution of a Landau-Type Operator
C. Malyshev
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 Dν(x) Dν(-x) at Re ν<0, x is real.
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