SOLUTIONS IN TERMS OF INTEGRALS OF MULTIVALUED FUNCTIONS FOR THE CLASSICAL HYPERGEOMETRIC EQUATIONS AND THE HYPERGEOMETRIC SYSTEM ON THE CONFIGURATION SPACE

The systems of differential equations associated with the classical hypergeometric functions and the hypergeometric functions on the space of point configurations are investigated from the viewpoint of the twisted de Rham theory. In each case, it is proved that the integral of a certain multivalued function over an arbitrary twisted (or loaded) cycle satisfies the system of differential equations in question. The classical hypergeometric functions studied here include Appell's hypergeometric functions F1, F2, F3, F4, Lauricella's hypergeometric functions FA, FB, FC, FD, and the generalized hypergeometric function n+1Fn.