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

2023/07/03 by Haraoka, Yoshishige, Ochiai, Hiroyuki, Sasaki, Takeshi +1
#33C05 #33C20 #34M03 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Primary 34A30 #Secondary 34M35

paper · doi:10.48550/arxiv.2307.01358

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.

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