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

Yoshishige Haraoka; Hiroyuki Ochiai; Takeshi Sasaki; Masaaki Yoshida

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

Classical Analysis and ODEs 2025-10-22 v3

Authors: Yoshishige Haraoka , Hiroyuki Ochiai , Takeshi Sasaki , Masaaki Yoshida

Abstract

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. They lead to assign the accessory parameter of $H_6$ a cubic polynomial of local exponents so that the equation has several nice symmetries. The other equations will be studied in the forthcoming papers.

Keywords

fuchsian differential equations singular points accessory parameter shift operators local exponents symmetries

Cite

@article{arxiv.2307.01358,
  title  = {Fuchsian differential equations of order 3,...,6 with three singular points and an accessory parameter},
  author = {Yoshishige Haraoka and Hiroyuki Ochiai and Takeshi Sasaki and Masaaki Yoshida},
  journal= {arXiv preprint arXiv:2307.01358},
  year   = {2025}
}

Comments

62 pages. accepted for publication in Funkcialaj Ekvacioj

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

Abstract

Keywords

Cite

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