Asymptotics of the hypergeometric function

An asymptotic representation is obtained for the hypergeometric function ${\bf F}(a+\lambda,b-\lambda,c,1/2-1/2z)$\nopagenumbers\end as $|\lambda|\rightarrow\infty$\nopagenumbers\end with $|{\rm ph}\,\lambda|<\pi$\nopagenumbers\end. It is uniformly valid in the z-plane cut in an appropriate way. Several other forms of the hypergeometric function are discussed also. Another representation which has some advantages over the conventional one is given as well. Copyright © 2001 John Wiley & Sons, Ltd.