Geodesic
Middle Convolution and Heun's Equation
Symmetry, integrability and geometry: methods and applications, Tome 5 (2009) Cet article a éte moissonné depuis la source Math-Net.Ru

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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 Painlevé equation. Middle convolutions of the Fuchsian system are related with an integral transformation of Heun's equation.
Keywords: Heun's equation; the space of initial conditions; the sixth Painlevé equation; middle convolution. 
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}
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Kouichi Takemura. Middle Convolution and Heun's Equation. Symmetry, integrability and geometry: methods and applications, Tome 5 (2009). http://geodesic.mathdoc.fr/item/SIGMA_2009_5_a39/

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