Special values of the hypergeometric function

Abstract

This thesis is about the Gauss hypergeometric function. Using Schwarz' theorem, we give a formula to calculate special values of the Gauss hypergeometric function; this formula involves a modular function with respect to a subgroup of the special linear group of dimension 2, this subgroup is commensurable with the modular group consisting of invertible 2-by-2 matrices with integer entries. Moreover, we use the analytic continuation of an identity of power series to find some more special values.