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 J. Sib. Fed. Univ. Math. Phys., 2014, Volume 7, Issue 3, Pages 339–346 (Mi jsfu380)

Conditions for convergence of the Mellin–Barnes integral for solution to system of algebraic equations

Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia

Abstract: In the article we consider the Mellin–Barnes integral that corresponds to a monomial function of a solution to a system of $n$ algebraic equations in $n$ unknowns. We obtain the necessary condition for the convergence domain of the integral to be non empty. For $n=2$ we prove that this condition is also sufficient.

Keywords: algebraic equations, Mellin–Barnes integral, convergence.

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UDC: 517.55
Accepted: 29.06.2014
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Citation: Vladimir R. Kulikov, “Conditions for convergence of the Mellin–Barnes integral for solution to system of algebraic equations”, J. Sib. Fed. Univ. Math. Phys., 7:3 (2014), 339–346

Citation in format AMSBIB
\Bibitem{Kul14} \by Vladimir~R.~Kulikov \paper Conditions for convergence of the Mellin--Barnes integral for solution to system of algebraic equations \jour J. Sib. Fed. Univ. Math. Phys. \yr 2014 \vol 7 \issue 3 \pages 339--346 \mathnet{http://mi.mathnet.ru/jsfu380} 

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This publication is cited in the following articles:
1. Artem V. Senashov, “On convergence of Mellin–Barnes integrals representing solutions of general algebraic systems of $3$ equations with $3$ variables”, Zhurn. SFU. Ser. Matem. i fiz., 10:3 (2017), 339–344
2. V. R. Kulikov, “A criterion for the convergence of the Mellin–Barnes integral for solutions to simultaneous algebraic equations”, Siberian Math. J., 58:3 (2017), 493–499
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