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

Yoshishige Haraoka, Hiroyuki Ochiai, Takeshi Sasaki, Masaaki Yoshida

Published 2023-07-03Version 1

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, which lead to assign the accessory parameter of $H_6$ a cubic polynomial of local exponents so that the equations have nice properties: shift operators and several symmetries. The other equations will be studied in the forthcoming papers.