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We consider the uniform asymptotic expansion for the Gauss hypergeometricfunction \[{}_2F_1(a+\epsilon\lambda,b;c+\lambda;x),\qquad 0<x<1\] as$\lambda\to+\infty$ in the neigbourhood of $\epsilon x=1$ when the parameter$\epsilon>1$ and the constants $a$, $b$ and $c$ are supposed finite. Use of astandard integral representation shows that the problem reduces toconsideration of a simple saddle point near an endpoint of the integrationpath. A uniform asymptotic expansion is first obtained by employing Bleistein'smethod. An alternative form of uniform expansion is derived following theapproach described in Olver's book [{\it Asymptotics and Special Functions},p.~346]. This second form has several advantages over the Bleistein form.

Uniform asymptotics of a Gauss hypergeometric function with two large parameters, V