Fuchsian differential equations of order 3,...,6 with three singular points and an accessory parameter

Yoshishige Haraoka; Hiroyuki Ochiai; Takeshi Sasaki; Masaaki Yoshida

paper

Fuchsian differential equations of order 3,...,6 with three singular points and an accessory parameter

arXiv:2307.01358

Abstract

Fuchsian differential equations $H_{j}$ of order $j = 3, \dots, 6$ with three singular points and one accessory parameter are presented. The shift operators for $H_{6}$ are studied. They lead to assign the accessory parameter of $H_{6}$ a cubic polynomial of local exponents so that the equation has several nice symmetries. The other equations will be studied in the forthcoming papers.

62 pages. accepted for publication in Funkcialaj Ekvacioj