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We obtain the asymptotic expansion for the Gauss hypergeometric function\[F(a-\lambda,b+\lambda;c+i\alpha\lambda;z)\] for $\lambda\rightarrow+\infty$with $a$, $b$ and $c$ finite parameters by application of the method ofsteepest descents. The quantity $\alpha$ is real, so that the denominatorialparameter is complex and $z$ is a finite complex variable restricted to lie inthe sector $|\arg (1-z)|<\pi$. We concentrate on the particular case $a=0$,$b=c=1$, which is associated with the Legendre functions of real degree andimaginary order. The resulting expansions are of Poincar\'e type and hold inrestricted domains of the $z$-plane. An expansion is given at the coalescenceof two saddle points. Numerical results illustrating the accuracy of thedifferent expansions are given.

Asymptotics of a Gauss hypergeometric function with large parameters,  III: Application to the Legendre functions of large imaginary order and real  degree