This article is cited in 3 papers

Approaches to the summability of divergent multidimensional integrals

G. M. Vainikko^a, I. K. Lifanov<sup>b

a</sup> Helsinki University of Technology
^b Institute of Numerical Mathematics, Russian Academy of Sciences

Abstract: Under discussion are various approaches to the concept of summability (finding the finite part – f.p. ) of divergent integrals with integrand represented as a product of two functions, one with a parameter-dependent non-integrable singularity at one point of the integration and the other absolutely integrable. A study is made of summability methods which are based on the expansion of the absolutely integrable function in a Taylor series with centre at the singular point (f.p.), on the analytic continuation with respect to the parameter of the singularity (a.f.p.), and on integration by parts (f.p.p.). Formulae of changes of variables in such integrals are presented.

UDC: 517

MSC: 26B20, 42B20

Received: 29.10.2002

DOI: 10.4213/sm760

 English version: Sbornik: Mathematics, 2003, 194:8, 1137–1166

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