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Analytic Error Function and Numeric Inverse Obtained by Geometric Means
Version 1
: Received: 27 February 2023 / Approved: 27 February 2023 / Online: 27 February 2023 (13:37:26 CET)
A peer-reviewed article of this Preprint also exists.
Martila, D.; Groote, S. Analytic Error Function and Numeric Inverse Obtained by Geometric Means. Stats 2023, 6, 431-437. Martila, D.; Groote, S. Analytic Error Function and Numeric Inverse Obtained by Geometric Means. Stats 2023, 6, 431-437.
Abstract
Using geometric considerations, we provide a clear derivation of the integral representation for the error function, known as the Craig formula. We calculate the corresponding power series expansion and prove the convergence. The same geometric means finally help to systematically derive handy formulas that approximate the inverse error function. Our approach can be used for applications in e.g. high-speed Monte Carlo simulations where this function is used extensively.
Keywords
error function; analytic function; inverse error function; approximations
Subject
PHYSICAL SCIENCES, General & Theoretical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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