Matsumoto, Keiji; Sasaki, Takeshi; Terasoma, Tomohide; Yoshida, Masaaki An example of Schwarz map of reducible Appell’s hypergeometric equation \(E_2\) in two variables. (English) Zbl 1370.33016 J. Math. Soc. Japan 69, No. 2, 563-595 (2017). This paper examines Appell’s hypergeometric functions \(F_1\) and \(F_2\), their series forms, integral representations and differential equations. Then the reducibility conditions on these Appell’s functions are examined. Then the systems of differential equations satisfied by these functions are looked into, and their complete solutions are obtained. Then monodromy representation, interaction matrices and circuit matrices are examined. The main purpose of this paper is to study the Schwarz map of Appell’s system for some specific parameter values. A connection of this Schwarz map for specified parameters to the Abel-Jacobi map is also shown and geometrical interpretations are also given. Reviewer: A. M. Mathai (Montreal) Cited in 2 Documents MSC: 33C65 Appell, Horn and Lauricella functions Keywords:Appell’s hypergeometric functions; reducibility; Schwarz map; birational map; Abel-Jacobi map; monodromy representation; circuit transformation; circuit matrices PDFBibTeX XMLCite \textit{K. Matsumoto} et al., J. Math. Soc. Japan 69, No. 2, 563--595 (2017; Zbl 1370.33016) Full Text: DOI arXiv Euclid