Asymptotic analysis of a family of polynomials associated with the inverse error function
| dc.creator | Dominici, Diego | |
| dc.creator | Knessl, Charles | |
| dc.date | 2008-11-13 | |
| dc.date.accessioned | 2026-07-07T10:18:21Z | |
| dc.date.available | 2026-07-07T10:18:21Z | |
| dc.description | 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. | |
| dc.description | 26 pages, 7 figures | |
| dc.identifier | https://arxiv.org/abs/0811.2243 | |
| dc.identifier | http://arxiv.org/abs/0811.2243 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174159 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 33B20 (primary) 34E20, 33E30 (secondary) | |
| dc.title | Asymptotic analysis of a family of polynomials associated with the inverse error function | |
| dc.type | text |