Asymptotic analysis of a family of polynomials associated with the inverse error function

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/174159We 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.26 pages, 7 figuresClassical Analysis and ODEs33B20 (primary) 34E20, 33E30 (secondary)Asymptotic analysis of a family of polynomials associated with the inverse error functiontext