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تسجيل مستخدم جديدThe asymptotics of a generalised Beta function
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تأليف
R. B. Paris
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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 $Re (p)>0$ 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.
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