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On solving general algebraic equations by integrals of elementary functions

E. N. Mikhalkin

Krasnoyarsk State University

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.

UDC: 517.55

Received: 19.02.2005

 English version: Siberian Mathematical Journal, 2006, 47:2, 301–306

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