A new method of obtaining integral transformation of the Heun equation is described. The Heun equation is reduced to the so-called hypergeometric system, a linear Fuchsian system of rank 3, and a Detweiler and Reiter algebraic analogue of the Katz middle convolution functor is applied. A linear Fuchsian system of rank 2 associated with the Heun equation is also studied.
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