论文标题
高斯高几何函数的均匀渐近学，有两个大参数v
Uniform asymptotics of a Gauss hypergeometric function with two large parameters, V
论文作者
论文摘要
We consider the uniform asymptotic expansion for the Gauss hypergeometric function \[{}_2F_1(a+ελ,b;c+λ;x),\qquad 0<x<1\] as $λ\to+\infty$ in the neigbourhood of $εx=1$ when the parameter $ε>1$ and the constants $a$, $b$ and $c$ are supposed有限。使用标准积分表示形式表明，该问题减少了集成路径终点附近的简单鞍点。首先是通过使用Bleistein的方法获得均匀的渐近扩张。根据Olver的书中描述的方法[{\ IT渐近函数和特殊功能}，第346页]，均匀扩展的替代形式。第二种形式比出血形式具有多个优点。
We consider the uniform asymptotic expansion for the Gauss hypergeometric function \[{}_2F_1(a+ελ,b;c+λ;x),\qquad 0<x<1\] as $λ\to+\infty$ in the neigbourhood of $εx=1$ when the parameter $ε>1$ and the constants $a$, $b$ and $c$ are supposed finite. Use of a standard integral representation shows that the problem reduces to consideration of a simple saddle point near an endpoint of the integration path. A uniform asymptotic expansion is first obtained by employing Bleistein's method. An alternative form of uniform expansion is derived following the approach described in Olver's book [{\it Asymptotics and Special Functions}, p.~346]. This second form has several advantages over the Bleistein form.
