Analytic Error Function and Numeric Inverse Obtained by Geometric Means

Dmitri Martila and Stefan Groote ()
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Dmitri Martila: Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, Estonia
Stefan Groote: Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, Estonia

Stats, 2023, vol. 6, issue 1, 1-7

Abstract: Using geometric considerations, we provided a clear derivation of the integral representation for the error function, known as the Craig formula. We calculated the corresponding power series expansion and proved the convergence. The same geometric means finally assisted in systematically deriving useful formulas that approximated the inverse error function. Our approach could be used for applications in high-speed Monte Carlo simulations, where this function is used extensively.

Keywords: error function; analytic function; inverse error function; approximations (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2023
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