What question did this study set out to answer?

To explore Fuchsian differential equations of orders 3 to 6 that have three singular points and an accessory parameter.

April 25, 2026Open Access

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

Key Points

To explore Fuchsian differential equations of orders 3 to 6 that have three singular points and an accessory parameter.
Introduced Fuchsian differential equations Hj of order j = 3, ..., 6.
Studied shift operators for H6 to analyze the accessory parameter.
Defined the accessory parameter as a cubic polynomial of local exponents.
Identified symmetries of the equations influenced by the accessory parameter for H6.
Established a framework for further exploration of related equations in upcoming papers.

Abstract

Fuchsian differential equations Hj 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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Cite This Study

Haraoka et al. (Wed,) studied this question.

synapsesocial.com/papers/69ec598788ba6daa22dab64e https://doi.org/https://doi.org/10.1619/fesi.69.1

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