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.