The asymptotics of a generalised Beta function

We consider the generalised Beta function introduced by Chaudhry {\it et al./} [J. Comp. Appl. Math. {\bf 78} (1997) 19–32] defined by $$B(x,y;p)={\int }_0^1{t}^{x-1}(1-t{)}^{y-1}\exp \left[\frac{-p}{4t(1-t)}\right]dt,$$ where $\mathrm{\Re }(p)>0$ and the parameters $x$ and $y$ are arbitrary complex numbers. The asymptotic behaviour of $B(x,y;p)$ is obtained when (i) $p$ large, with $x$ and $y$ fixed, (ii) $x$ and $p$ large, (iii) $x$, $y$ and $p$ large and (iv) either $x$ or $y$ large, with $p$ finite. Numerical results are given to illustrate the accuracy of the formulas obtained.