ABSTRACT
In this section and 87 and 8 the general procedure is illustrated by various exanlples. 6.2 When neither of the parameters a and b is zero or a negative integer the hypergeometric function F(a, b; c; z) is given by
compare Chapter 5, 59.1. In accordance with the final equation of the preceding subsection, we consider the integral representation
The choice of endpoints of the path %' is not crucial: we take them to be + ioo. The important feature is that the poles of the integrand at 0,1,2, ... are on one side of 4andtheotherpoles -a, -a-1, -a-2 ,... and -6, -b-1, -b-2 ,... areon the opposite side; see the continuous curve in Fig. 6.1. Since, by hypothesis, neither a nor b is zero or a negative integer it is always possible to choose %'in this way.
