This function maps the upper half-plane to a spherical triangle if α + β + γ > 1, or a hyperbolic triangle if α + β + γ < 1. When α + β + γ = 1, then the triangle is a Euclidean triangle with straight edges: a = 0, _2 F_1 \left(a, b; c; z\right) = 1, and the formula reduces to that given by the Schwarz–Christoffel transformation.
