Mathematics

Asymptotics of three-dimensional integrals singularly depending on a small parameter

A. A. Ershov

Chelyabinsk State University, Chelyabinsk, Russia

Abstract: Asymptotics of some three-dimensional integrals singularly depending on a small parameter is constructed. The integrand denominator of the considered integrals is a sum of a small parameter and nonnegative function vanishing on three not intersecting surfaces. Such form integrals diverge as a small parameter tends to zero. The method of singularities subtraction and the circle method are applied.

Keywords: asymptotic expansion, small parameter, integral, singularities subtraction method, circle method.

UDC: 517.9

Received: 11.11.2014
Revised: 10.02.2016

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