Let ''πα'', ''πβ'', and ''πγ'' be the interior angles at the vertices of the triangle in [[radians]]. Each of ''α'', ''β'', and ''γ'' may take values between 0 and 1 inclusive. Following Nehari,{{harvsfn|Nehari|1975|page=309}}, these angles are in clockwise order, with the vertex having angle ''πα'' at the origin and the vertex having angle ''πγ'' lying on the real line. The Schwarz triangle function can be given in terms of [[hypergeometric functions]] as:
This formula can be derived using the [[Schwarzian derivative]]. Through the theory of complex [[ordinary differential equation]]s with [[regular singular point]]s and the [[Schwarzian derivative]], the triangle function can be expressed as the quotient of two solutions of a [[hypergeometric differential equation]] with real coefficients and singular points at 0, 1 and ∞. By the [[Schwarz reflection principle]], the reflection group induces an action on the two dimensional space of solutions. On the orientation-preserving normal subgroup, this two-dimensional representation corresponds to the [[monodromy]] of the ordinary differential equation and induces a group of [[Möbius transformation]]s on quotients of [[hypergeometric function]]s.{{sfn|Nehari|1975|pp=198-208}}
