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On solving general algebraic equations by integrals of elementary functions

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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.

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References

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Authors and Affiliations

  1. Krasnoyarsk State University, Krasnoyarsk, Russia

    E. N. Mikhalkin

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  1. E. N. Mikhalkin
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Original Russian Text Copyright © 2006 Mikhalkin E. N.

The author was supported by the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-1212.2003.1).

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Translated from Sibirski \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Matematicheski \(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Zhurnal, Vol. 47, No. 2, pp. 365–371, March–April, 2006.

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Mikhalkin, E.N. On solving general algebraic equations by integrals of elementary functions. Sib Math J 47, 301–306 (2006). https://doi.org/10.1007/s11202-006-0043-4

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  • DOI: https://doi.org/10.1007/s11202-006-0043-4

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