Asymptotic analysis of the derivatives of the inverse error function

Details Asymptotic analysis of the derivatives of the inverse error function Asymptotic analysis of the derivatives of the inverse error function

2006-07-09

arxiv.org/abs/math/0607230v2

Mathematics

Classical Analysis and ODEs

25 pages, 6 figures

Scientific paper

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.

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