On a fundamental system of solutions of a certain hypergeometric equation

2014/07/30 by Teruhisa Tsuda, Tsuda, Teruhisa
Computer Science · Mathematics · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Waves and Solitons #Numerical methods for differential equations #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1407.8052

openalex publication_date 2014/07/30 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We study the linear Pfaffian systems satisfied by a certain class of hypergeometric functions, which includes Gauß's ₂ F₁, Thomae's _L F_L-1 and Appell-Lauricella's F_D. In particular, we present a fundamental system of solutions with a characteristic local behavior by means of Euler-type integral representations. We also discuss how they are related to the theory of isomonodromic deformations or Painlevé equations.

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