Solution of fifth-degree equations
type: Item
instance of: scholarly article
title: Solution of fifth-degree equations
zbMATH Open document ID: 1241.12001
DOI: 10.3103/S1066369X09060036
published in: Russian Mathematics
publication date: 2009-10-26T00:00:00Z
review text: The authors establish a relationship between two approaches to the solution of algebraic fifth-degree equations, namely, the Hermite-Kronecker method (based on the modular elliptic equation) and the Mellin method (based on hypergeometric series). They solve the modular equation on the base of the Semusheva--Tsikh formula [\textit{A. Yu. Semusheva} and \textit{A. K. Tsikh}, Complex analysis and differential operators. Krasnoyarsk: Krasnoyarskii Gos. Univ., 134--146 (2000)], and then they deduce a formula for a series solution of the general fifth degree equation reduced by the Tschirnhaus transform \(y^5+5y=a\) and determine the convergence domain.
reviewed by: Olaf Ninnemann
Mathematics Subject Classification ID: 12E10
Mathematics Subject Classification ID: 30C15
Mathematics Subject Classification ID: 11F12
Mathematics Subject Classification ID: 33C65
zbMATH DE Number: 5621425
author: Evgeny Mikhalkin
MaRDI profile type: Publication
cites work: Q3235831
cites work: Multiple Mellin-Barnes integrals as periods of Calabi-Yau manifolds with several moduli
cites work: Q5437059
cites work: Q4669635
full work available at URL: s1066369x09060036
OpenAlex ID: W2100886404
description: scientific article; zbMATH DE number 5621425