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J. Sib. Fed. Univ. Math. Phys., 2012, Volume 5, Issue 2, Pages 230–238 (Mi jsfu235)  

This article is cited in 1 scientific paper (total in 1 paper)

Certain formulas for solutions to trinomial and tetranomial algebraic equations

Evgeny N. Mikhalkin

Institute of Mathematics, Siberian Federal University, Krasnoyarsk, Russia

Abstract: Algebraic equations with one and two parameters are considered. We prove that solutions to such equations can be represented as linear combination of generalized hypergeometric series. This result allows to express (nonlinearly) solutions to cubic and quartic equations by Gauss hypergeometric series.

Keywords: algebraic equation, Gauss hypergeometric series, generalized hypergeometric series.

Full text: PDF file (177 kB)
References: PDF file   HTML file
UDC: 517.55+517.588
Received: 15.09.2011
Received in revised form: 30.10.2011
Accepted: 30.12.2011

Citation: Evgeny N. Mikhalkin, “Certain formulas for solutions to trinomial and tetranomial algebraic equations”, J. Sib. Fed. Univ. Math. Phys., 5:2 (2012), 230–238

Citation in format AMSBIB
\Bibitem{Mik12}
\by Evgeny~N.~Mikhalkin
\paper Certain formulas for solutions to trinomial and tetranomial algebraic equations
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2012
\vol 5
\issue 2
\pages 230--238
\mathnet{http://mi.mathnet.ru/jsfu235}


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    This publication is cited in the following articles:
    1. V. I. Shmoilov, M. V. Khisamutdinov, G. A. Kirichenko, “Reshenie algebraicheskikh uravnenii metodom Rutiskhauzera–Nikiportsa”, Vestn. NGU. Ser. matem., mekh., inform., 15:1 (2015), 63–79  mathnet
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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