Fuchsian Differential Equations of Order 3, ..., 6 with Three Singular Points and an Accessory Parameter

Abstract

Fuchsian differential equations H_j of order j = 3, ..., 6 with three singular points and one accessory parameter are presented. The shift operators for H₆ are studied. They lead to assign the accessory parameter of H₆ a cubic polynomial of local exponents so that the equation has several nice symmetries. The other equations will be studied in the forthcoming papers.