Asymptotic analysis of the derivatives of the inverse error function
| dc.creator | Dominici, Diego | |
| dc.date | 2006-07-09 | |
| dc.date | 2007-06-05 | |
| dc.date.accessioned | 2026-07-07T08:08:01Z | |
| dc.date.available | 2026-07-07T08:08:01Z | |
| dc.description | The inverse of the error function, $\operatorname{inverf}(x),$ has applications in diffusion problems, chemical potentials, ultrasound imaging, etc. We analyze the derivatives $\frac{d^{n}}{dz^{n}} \operatorname*{inverf}(z) |_{z=0}$, as $n\to \infty$ using nested derivatives and a discrete ray method. We obtain a very good approximation of $\operatorname{inverf}(x)$ through a high-order Taylor expansion around $x=0$. We give numerical results showing the accuracy of our formulas. | |
| dc.description | 25 pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/math/0607230 | |
| dc.identifier | http://arxiv.org/abs/math/0607230 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131122 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 33B20 (Primary); 30B10, 34K25 (Secondary) | |
| dc.title | Asymptotic analysis of the derivatives of the inverse error function | |
| dc.type | text |