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