Petersburg Department of Steklov Institute of Mathematics

PREPRINT 4/2001

THE INTEGRAL REPRESENTATION FOR THE PRODUCT OF TWO PARABOLIC CYLINDER FUNCTIONS $D_\nu(x)D_\nu(-x)$ AT $\Re\nu<0$ BY MEANS OF THE FUNDAMENTAL SOLUTION OF A LANDAU-TYPE OPERATOR

This preprint was accepted May 30, 2001
Contact: 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
$D_\nu(x)D_\nu(-x)$ at $\Re\nu<0$, $x\in\Bbb R$.