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Analytic Error Function and Numeric Inverse Obtained by Geometric Means

Author

Listed:
  • Dmitri Martila

    (Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, Estonia
    These authors contributed equally to this work.)

  • Stefan Groote

    (Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, Estonia
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Dmitri Martila & Stefan Groote, 2023. "Analytic Error Function and Numeric Inverse Obtained by Geometric Means," Stats, MDPI, vol. 6(1), pages 1-7, March.
    • Handle: RePEc:gam:jstats:v:6:y:2023:i:1:p:26-437:d:1098315
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