Analytic Error Function and Numeric Inverse Obtained by Geometric Means
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 us...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Stats |
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| Online Access: | https://www.mdpi.com/2571-905X/6/1/26 |
| _version_ | 1797608939485921280 |
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| author | Dmitri Martila Stefan Groote |
| author_facet | Dmitri Martila Stefan Groote |
| author_sort | Dmitri Martila |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T05:54:41Z |
| format | Article |
| id | doaj.art-c9885df7ba1d4fc59da14c6225278b8f |
| institution | Directory Open Access Journal |
| issn | 2571-905X |
| language | English |
| last_indexed | 2024-03-11T05:54:41Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Stats |
| spelling | doaj.art-c9885df7ba1d4fc59da14c6225278b8f2023-11-17T13:54:05ZengMDPI AGStats2571-905X2023-03-016143143710.3390/stats6010026Analytic Error Function and Numeric Inverse Obtained by Geometric MeansDmitri Martila0Stefan Groote1Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, EstoniaInstitute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, EstoniaUsing 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.https://www.mdpi.com/2571-905X/6/1/26error functionanalytic functioninverse error functionapproximations |
| spellingShingle | Dmitri Martila Stefan Groote Analytic Error Function and Numeric Inverse Obtained by Geometric Means Stats error function analytic function inverse error function approximations |
| title | Analytic Error Function and Numeric Inverse Obtained by Geometric Means |
| title_full | Analytic Error Function and Numeric Inverse Obtained by Geometric Means |
| title_fullStr | Analytic Error Function and Numeric Inverse Obtained by Geometric Means |
| title_full_unstemmed | Analytic Error Function and Numeric Inverse Obtained by Geometric Means |
| title_short | Analytic Error Function and Numeric Inverse Obtained by Geometric Means |
| title_sort | analytic error function and numeric inverse obtained by geometric means |
| topic | error function analytic function inverse error function approximations |
| url | https://www.mdpi.com/2571-905X/6/1/26 |
| work_keys_str_mv | AT dmitrimartila analyticerrorfunctionandnumericinverseobtainedbygeometricmeans AT stefangroote analyticerrorfunctionandnumericinverseobtainedbygeometricmeans |