2005/01/25 by Kouichi Takemura, Takemura, Kouichi
Computer Science · Mathematics · Physics and Astronomy · #33E10 #34M55 #82B23 #Advanced Algebra and Geometry #Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Matrix Theory and Algorithms #Quantum Algebra (math.QA) #math-ph #math.CA #math.MP #math.QA #msc:33E10 #msc:34M55 #msc:82B23 #nlin.SI
paper · pdf · doi:10.48550/arxiv.math/0501428
28 pages
arxiv created 2005/01/25 · openalex publication_date 2005/01/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Several results on Heun's equation are generalized to a certain class of Fuchsian differential equations. Namely, we obtain integral representations of solutions and develop Hermite-Krichever Ansatz on them. In particular, we investigate linear differential equations that produce Painlevé equation by monodromy preserving deformation and obtain solutions of the sixth Painlevé equation which include Hitchin's solution. The relationship with finite-gap potential is also discussed.