一类与逆误差函数相关的多项式族的渐近分析
Asymptotic analysis of a family of polynomials associated with the inverse error function
摘要：
我们分析了微分差分方程$P_{n+1}(x)=P_{n}^{\prime}(x)+x(n+1)P_{n}(x)$定义的多项式序列渐近为$n\to\infty$ .多项式$P_{n}(x)$在计算逆误差函数$\operatorname{inverf}(x)$的高阶导数时出现。我们使用奇异性分析和离散版本的WKB和射线方法，并给出数值结果，显示我们的公式的准确性。
英文摘要：
We analyze the sequence of polynomials defined by the differential-difference equation $P_{n+1}(x)=P_{n}^{\prime}(x)+x(n+1)P_{n}(x)$ asymptotically as $n\to\infty$. The polynomials $P_{n}(x)$ arise in the computation of higher derivatives of the inverse error function $\operatorname{inverf}(x)$. We use singularity analysis and discrete versions of the WKB and ray methods and give numerical results showing the accuracy of our formulas.
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