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We consider the asymptotic behaviour of the generalised hypergeometricfunction \[{}_3F_2\bl(\!\!\begin{array}{c} 1, (1+t)k/2, (1+t)k/2+1/2\\tk+1,k+1\end{array}\!\!; x\br),\qquad 0<x,t\leq 1\] as the parameter $k\to+\infty$.Numerical results illustrating the accuracy of the resulting expansion aregiven.

Asymptotics of a ${}_3F_2$ hypergeometric function with four large parameters