Middle Convolution and Heun's Equation - Kouichi Takemura (Symmetry, Integrability and Geometry: Methods and Applications, 2009)
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.