Asymptotic analysis of the derivatives of the inverse error function

2006/07/09 by Diego Dominici, Dominici, Diego
Computer Science · Mathematics · Physics and Astronomy · #30B10 #33B20 (Primary) #34K25 (Secondary) #Advanced X-ray Imaging Techniques #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Matrix Theory and Algorithms #Numerical methods in inverse problems #math.CA #msc:30B10 #msc:33B20 #msc:34K25

paper · pdf · doi:10.48550/arxiv.math/0607230

25 pages, 6 figures

openalex publication_date 2006/07/09 · arxiv created 2007/06/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The inverse of the error function, inverf(x), has applications in diffusion problems, chemical potentials, ultrasound imaging, etc. We analyze the derivatives \fracdⁿdzⁿ \operatorname*inverf(z) |_z=0, as n→ ∞ using nested derivatives and a discrete ray method. We obtain a very good approximation of 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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