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Mathematics of Computation

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Formulas for calculating the error function of a complex variable


Author: H. E. Salzer
Journal: Math. Comp. 5 (1951), 67-70
MSC: Primary 65.0X
DOI: https://doi.org/10.1090/S0025-5718-1951-0048150-3
Corrigendum: Math. Comp. 6 (1952), 61.
MathSciNet review: 0048150
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    J. Burgess, “On the definite integral $\frac {2}{{\sqrt \pi }}\int _0^t {{e^{ - {t^2}}}dt}$ with extended tables of values,” R. Soc. Edinburgh, Trans., v. 39, part II, 1898, p. 257-321. J. R. Airey, “The ’converging factor’ in asymptotic series and the calculation of Bessel, Laguerre and other functions,” Phil. Mag., s. 7, v. 24, 1937, p. 521-552. W. L. Miller & A. R. Gordon, “Numerical evaluation of infinite series,” Jn. Phys. Chem., v. 35, 1931, especially part V, p. 2856-2857, 2860-2865. J. B. Rosser, Theory and Application of $\int _0^z {{e^{ - {x^2}}}dx}$ and $\int _0^z {{e^{ - {p^2}{y^2}}}} dy\int _0^y {{e^{ - {x^2}}}dx}$. Part I. Methods of Computation, New York, 1948. E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals. Oxford, 1937, p. 60-64. E. T. Whittaker & G. N. Watson, A Course of Modern Analysis. Fourth ed., Cambridge, 1940, p. 124, 474-476.
  • E. T. Goodwin, The evaluation of integrals of the form $\int ^\infty _{-\infty } f(x) e^{-x^{2}} dx$, Proc. Cambridge Philos. Soc. 45 (1949), 241–245. MR 29281, DOI https://doi.org/10.1017/s0305004100024786
  • A. M. Turing, A method for the calculation of the zeta-function, Proc. London Math. Soc. (2) 48 (1943), 180–197. MR 9612, DOI https://doi.org/10.1112/plms/s2-48.1.180
  • H. G. Dawson, “On the numerical value of $\int _0^h {{e^{{x^2}}}dx}$,” London Math. Soc., Proc., s. 1, v. 29, 1898, p. 519-522. NBS, Tables of Probability Functions. V. 1, New York, 1941.

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Article copyright: © Copyright 1951 American Mathematical Society