The monodromy representation and twisted period relations for Appell's hypergeometric function F₄

2013/10/16 by Yoshiaki Goto, Goto, Yoshiaki, Keiji Matsumoto +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #32G20 #32S40 #33C65 #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1310.4243

openalex publication_date 2013/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the system F₄(a,b,c) of differential equations annihilating Appell's hypergeometric series F₄(a,b,c;x). We find the integral representations for four linearly independent solutions expressed by the hypergeometric series F₄. By using the intersection forms of twisted (co)homology groups associated with them, we provide the monodromy representation of F₄(a,b,c) and the twisted period relations for the fundamental systems of solutions of F₄.

Cited by

• The monodromy representation of a hypergeometric system in m variables of rank p^m

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