On closed-form integration of some Fuchsian differential equations related to a conformal mapping of circular pentagons with a cut (Q610309)

Let \(D\) be a sector of a disk \(U\) with a radial cut beginning at the center of \(U\). The author explicitly constructs a conformal mapping of the pentagon \(D\) onto the upper half--plane in terms of particular solutions of Fuchs type differential equations.