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Petersburg Department of Steklov Institute of Mathematics

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PREPRINT 4/2001

C. MALYSHEV
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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 $\Re\nu<0$, $x\in\Bbb R$.

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