Formulas for calculating the error function of a complex variable

Salzer, H. E.

doi:10.1090/S0025-5718-1951-0048150-3

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
Full-text PDF

[1] 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.
[2] 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.
[3] 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.
[4] 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.
[5] E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals. Oxford, 1937, p. 60-64.
[6] E. T. Whittaker & G. N. Watson, A Course of Modern Analysis. Fourth ed., Cambridge, 1940, p. 124, 474-476.
[7] E. T. Goodwin, The evaluation of integrals of the form ∫^{∞}_{-∞}𝑓(𝑥)𝑒^{-𝑥²}𝑑𝑥, Proc. Cambridge Philos. Soc. 45 (1949), 241–245. MR 0029281
[8] A. M. Turing, A method for the calculation of the zeta-function, Proc. London Math. Soc. (2) 48 (1943), 180–197. MR 0009612, https://doi.org/10.1112/plms/s2-48.1.180
[9] 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.
[10] NBS, Tables of Probability Functions. V. 1, New York, 1941.