Connection Problem for the Generalized Hypergeometric Function

抄録

The generalized hypergeometric function has three singular points 0, 1, and ∞. Connection problem between fundamental solutions at 0 and ∞ was completely solved. However, connection problem between fundamental solutions at 0 and 1 has been not completely solved because of holomorphic solutions at 1. In this paper, we solve connection problem between fundamental solutions at singular points 0 and 1 for the generalized hypergeometric function, using analytic continuation of the integral representation. Namely, all connection coefficients are products of the sine and the cosecant. In other words, we give a good fundamental system of solutions at 1.