1. An asymptotic expansion for the hypergeometric function 2F1(a,b;c;x)
2. Asymptotic expansion of 2F1(a,b;c;x) in terms of confluent hypergeometric functions
3. An expansion of the hypergeometric function in Bessel functions
4. See, e.g.,Higher Transcendental Functions, edited by A. Erdélyi (McGraw-Hill, New York, 1953), Vol. 1, Chap. 1.6.(2), p. 13.
5. The saddle-point method, also called the method of steepest descent, for asymptotic evaluation of an integral, is treated in many books. A classical reference is A. Erdélyi,Asymptotic Expansions(Dover, New York, 1956). Our application, although apparently multidimensional, involves a product of one-dimensional integrals with the saddle-point integrations along the real or imaginary directions.