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Title:
Middle Convolution and Heun's Equation
Authors:
Takemura, Kouichi
Publication:
eprint arXiv:0810.3112
Publication Date:
10/2008
Origin:
ARXIV
Keywords:
Mathematics - Classical Analysis and ODEs, Mathematical Physics, Nonlinear Sciences - Exactly Solvable and Integrable Systems, 34M35, 33E10, 34M55
Comment:
SIGMA 5 (2009), 040, 22 pages; doi:10.3842/SIGMA.2009.040
Bibliographic Code:
2008arXiv0810.3112T

Abstract

Heun's equation naturally appears as special cases of Fuchsian system of differential equations of rank two with four singularities by introducing the space of initial conditions of the sixth Painlev\'e equation. Middle convolutions of the Fuchsian system are related with an integral transformation of Heun's equation.
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