2017 年 60 巻 1 号 p. 77-132
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.