In [Temme N.M., Special functions. An introduction to the classical functions of mathematical physics, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1996, Section 11.3.3.1] a uniform asymptotic expansion for the incomplete beta function was derived. It was not obvious from those results that the expansion is actually an asymptotic expansion. We derive a remainder estimate that clearly shows that the result indeed has an asymptotic property, and we also give a recurrence relation for the coefficients.
翻译：在[Temme N.M., 特殊功能., 数学物理学古典功能的介绍,A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1996, New York, 1996, 第11.3.3.1节] 中,得出了不完全的贝塔功能的统一无药可治的扩展,从这些结果中看不出这种扩展实际上是一种无药可治的扩展。我们得出的剩余估计数清楚地表明,结果确实具有无药可治的特性,我们还给出了系数的复现关系。
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