Nakagiri's Monodromy Representations Associated with Appell's Hypergeometric Functions F₂ and F₃

Abstract

We study monodromy representations associated with Appell's hypergeometric functions F₂ and F₃ by using integrals of multivalued functions. In particular, we derive Nakagiri's matix elements of the representations in a different manner and relax his conditions on the parameters. As an application, we give a simple and elementary derivation of sufficient conditions that the systems of differential equations satisfied by F₂ and F₃ are irreducible.