On the calculation of the inverse of the error function

Author:
Anthony Strecok

Journal:
Math. Comp. **22** (1968), 144-158

MSC:
Primary 65.25

DOI:
https://doi.org/10.1090/S0025-5718-1968-0223070-2

MathSciNet review:
0223070

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Abstract | References | Similar Articles | Additional Information

Abstract: Formulas are given for computing the inverse of the error function to at least 18 significant decimal digits for all possible arguments up to in magnitude.

A formula which yields to at least 22 decimal places for is also developed.

**[1]**R. A. Fisher & E. A. Cornish, "The percentile points of distributions having known cumulants,"*Technometrics*, v. 2, 1960, pp. 209-223.**[2]**H. Goldberg & H. Levine, "Approximate formulas for the percentage points and normalization of and ,"*Ann. Math. Statistics*, v. 17, 1946, pp. 216-225. MR**8**, 42. MR**0016611 (8:42j)****[3]**J. Wishart, " probabilities for large numbers of degrees of freedom,"*Biometrika*, v. 43, 1956, pp. 92-95. MR**18**, 78. MR**0079385 (18:78d)****[4]**E. Paulson, "An approximate normalization of the analysis of variance distribution,"*Ann. Math. Statistics*, v. 13, 1942, pp. 233-235. MR**4**, 23. MR**0006668 (4:23g)****[5]**J. R. Philip, "The function inverfc ,"*Austral. J. Phys.*, v. 13, 1960, pp. 13-20. MR**22**#9626. MR**0118857 (22:9626)****[6]**L. Carlitz, "The inverse of the error function,"*Pacific J. Math.*, v. 13, 1963, pp. 459-470. MR**27**#3839. MR**0153878 (27:3839)****[7]**H. Kuki,*Mathematical Functions, a Description of the Center's*7094 FORTRAN II*Mathematical Function Library*, University of Chicago Computation Center, February 1966, pp. 205-214.**[8]**J. B. Rosser,*Theory and Application of and*, Part 1: Methods of Computation, ORSD 5861, Mapleton House, Brooklyn, N. Y., 1948, p. 32. MR**10**, 267. MR**0027176 (10:267e)****[9]**H. Wall,*Analytic Theory of Continued Fractions*, Van Nostrand, Princeton, N. J., 1948, p. 358. MR**10**, 32. MR**0025596 (10:32d)****[10]**H. C. Thacher, Jr., "Conversion of a power to a series of Chebyshev polynomials,"*Comm. ACM*, v. 7, 1964, pp. 181, 182.**[11]**C. Hastings,*Approximations for Digital Computers*, Princeton Univ. Press, Princeton, N. J., 1955, pp. 191-192. MR**16**, 963. MR**0068915 (16:963e)****[12]**F. B. Hildebrand,*Introduction to Numerical Analysis*, McGraw-Hill, New York, 1956, pp. 389-395. MR**17**, 788. MR**0075670 (17:788d)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1968-0223070-2

Article copyright:
© Copyright 1968
American Mathematical Society