Asymptotic expansions of the Gauss hypergeometric function with large parameters, $F(\unicode[STIX]{x1D6FC}+\unicode[STIX]{x1D716}_{1}\unicode[STIX]{x1D70F},\unicode[STIX]{x1D6FD}+\unicode[STIX]{x1D716}_{2}\unicode[STIX]{x1D70F};\unicode[STIX]{x1D6FE}+\unicode[STIX]{x1D716}_{3}\unicode[STIX]{x1D70F};z)$ as $|\unicode[STIX]{x1D70F}|\rightarrow \infty$, are known for many special cases, but not for one that the author encountered in recent work on fluid mechanics: $\unicode[STIX]{x1D716}_{2}=0$ and $\unicode[STIX]{x1D716}_{3}=\unicode[STIX]{x1D716}_{1}z$. This paper gives the leading term for that case if $\unicode[STIX]{x1D6FD}$ is not a negative integer and $z$ is not on the branch cut $[1,\infty )$, and it shows how subsequent terms can be found.

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具有两个大参数的高斯超几何函数的渐近：一个新案例

大参数高斯超几何函数的渐近展开，$F(\unicode[STIX]{x1D6FC}+\unicode[STIX]{x1D716}_{1}\unicode[STIX]{x1D70F},\unicode[STIX]{x1D6FD}+\unicode[STIX]{x1D716} _{2}\unicode[STIX]{x1D70F};\unicode[STIX]{x1D6FE}+\unicode[STIX]{x1D716}_{3}\unicode[STIX]{x1D70F};z)$作为$|\unicode[STIX]{x1D70F}|\rightarrow \infty$，以许多特殊情况而闻名，但不是作者在最近的流体力学工作中遇到的一种情况：$\unicode[STIX]{x1D716}_{2}=0$和$\unicode[STIX]{x1D716}_{3}=\unicode[STIX]{x1D716}_{1}z$. 本文给出了该案例的主要术语，如果$\unicode[STIX]{x1D6FD}$不是负整数并且$z$不在树枝上$[1,\infty)$，它显示了如何找到后续项。