The monodromy representation and twisted period relations for Appell’s hypergeometric function F 4

We consider the system F 4 (a, b, c) of differential equations annihilating Appell's hypergeometric series F 4 (a,b,c;x) . We find the integral representations for four linearly independent solutions expressed by the hypergeometric series F 4 . By using the intersection forms of twisted (co)homology groups associated with them, we provide the monodromy representation of F 4 (a, b, c) and the twisted period relations for the fundamental systems of solutions of F 4 .