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

This article is cited in 2 scientific papers (total in 2 papers)

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

Vladimir R. Kulikov

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.

Full text: PDF file (158 kB)
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UDC: 517.55
Received: 10.05.2014
Received in revised form: 10.06.2014
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  mathnet  crossref
    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  mathnet  crossref  crossref  isi  elib  elib
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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