Asymptotic analysis of the derivatives of the inverse error function

Abstract

The inverse of the error function, $\mathrm{inverf}(x),$ has applications in diffusion problems, chemical potentials, ultrasound imaging, etc. We analyze the derivatives $\frac{d^n}{d{z}^n}\mathrm{inverf}(z){|}_{z=0}$, as $n\to \infty$ using nested derivatives and a discrete ray method. We obtain a very good approximation of $\mathrm{inverf}(x)$ through a high-order Taylor expansion around $x=0$. We give numerical results showing the accuracy of our formulas.

25 pages, 6 figures

References in corpus (2)

• The Andante Regime of Scalar Field Dynamics
• Lifetimes of agents under external stress