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Middle Convolution and Heun's Equation

Keywords: Heun's equation , the space of initial conditions , the sixth Painlevé equation , middle convolution

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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.


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