Algebraic Equations and Hypergeometric Series

Mikael Passare and August Tsikh

A chapter in The Legacy of Niels Henrik Abel, 2004, pp 653-672 from Springer

Abstract: Abstract We study the solutions of a general n th order algebraic equation represented by multidimensional hypergeometric series. We provide a detailed description of the domains of convergence of these series in terms of the amoeba and the Horn-Kapranov uniformization of the corresponding discriminant. From a geometric viewpoint this amounts to describing the maximal Reinhardt domains in the complement of the discriminant locus.

Keywords: Series Solution; Hypergeometric Series; Convergence Domain; Discriminant Locus; Sylvester Matrix (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18908-1_21

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DOI: 10.1007/978-3-642-18908-1_21

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