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Heun equation and Painlevé equation | Kouichi Takemura
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15 Mar 2005 | Subject: | Classical Analysis and ODEs; Quantum Algebra; Exactly Solvable and Integrable Systems; Mathematical Physics MSC-class: 33E10,34M55 | math.CA math-ph math.MP math.QA nlin.SI | Abstract: | We relate two parameter solutions of the sixth Painlevé equation and finite-gap solutions of the Heun equation by considering monodromy on a certain class of Fuchsian differential equations. In the appendix, we present formulae on differentials of elliptic modular functions, and obtain the ellitic form of the sixth Painlevé equation directly. | Source: | arXiv, math.CA/0503288 | Services: | Forum | Review | PDF | Favorites |
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