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Siberian Mathematical Journal

, Volume 47, Issue 2, pp 301–306 | Cite as

On solving general algebraic equations by integrals of elementary functions

  • E. N. Mikhalkin
Article

Abstract

We obtain an integral formula for a solution to a general algebraic equation. In this formula the integrand is an elementary function and integration is carried out over an interval. The advantage of this formula over the well-known Mellin formula is that the integral has a broader convergence domain. This circumstance makes it possible to describe the monodromy of a solution for trinomial equations.

Keywords

algebraic equation integral representation hypergeometric function 

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References

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    Mellin H. J., “Résolution de l’equation algébrique générale á l’aide de la fonction gamma,” C. R. Acad. Sci. Paris Sér. I Math., 172, 658–661 (1921).zbMATHGoogle Scholar
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    Passare M. and Tsikh A., “Algebraic equations and hypergeometric series,” in: The Legacy of Niels Henrik Abel, Springer-Verlag, Berlin; Heidelberg, 2004, pp. 653–672.Google Scholar
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    Zhdanov O. N. and Tsikh A. K., “Studying the multiple Mellin-Barnes integrals by means of multidimensional residues,” Siberian Math. J., 39, No. 2, 245–260 (1998).MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • E. N. Mikhalkin
    • 1
  1. 1.Krasnoyarsk State UniversityKrasnoyarskRussia

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