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On the evaluation of integrals related to the error function


Authors: C. Chiarella and A. Reichel
Journal: Math. Comp. 22 (1968), 137-143
MSC: Primary 65.25
DOI: https://doi.org/10.1090/S0025-5718-1968-0223068-4
MathSciNet review: 0223068
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  • [1] D. Posener, Austral. J. Phys., v. 12, 1959, pp. 184-196.
  • [2] G. D. Finn & D. Mugglestone, Monthly Notices Roy. Astronom. Soc., 129, 1965, no. 2, p. 222.
  • [3] J. T. Davies & J. M. Vaughan, Aslrophys. J., v. 137, 1963, p. 1302.
  • [4] V. J. Bell, P. A. C. Buckler & I. C. Pull, U. K. Atomic Energy Authority Report H.M.S.O. (Atomic Energy Establishment, Winfrith), 1963.
  • [5] J. L. Cook & D. Elliot, Austral. J. Appl. Sci., v. 11, 1960, pp. 16-32. MR 22 #6130. MR 0115328 (22:6130)
  • [6] D. G. Hummer, Mem. Roy. Astronom. Soc., v. 70, 1965, pp. 1-31. MR 34 #928. MR 0201043 (34:928)
  • [7] J. B. Rosser, Theory and A pplication of $ \int {_0^z} {e^{ - x2}}dx$ and $ \int {_0^z{e^{ - \rho 2y2}}dy} \int {_0^y{e^{ - x2}}dx} $. Part I : Methods of Compulation, Mapleton House, Brooklyn, N. Y, 1948. MR 10, 267. MR 0027176 (10:267e)
  • [8] H. E. Salzer, MTAC, v. 5, 1951, pp. 67-70. MR 13, 989.
  • [9] O. N. Strand, Math. Comp., v. 19, 1965, pp. 127-129. MR 30 #694. MR 0170456 (30:694)
  • [10] V. N. Faddeyeva & N. M. Terent'ev, Tables of Values of the Function $ w(z) = {e^{ - {z^2}}}(1 + 2i{\pi ^{ - 1/2}}\int {_0^z{e^{{t^2}}}dt} )$ for Complex Argument, translated from the Russian, Pergamon Press, Oxford, 1961. MR 22 #12740. MR 0122013 (22:12740)
  • [11] B. D. Fried & S. D. Conte, The Plasma Dispersion Function, Academic Press, New York, 1961. MR 24 #B1958. MR 0135916 (24:B1958)
  • [12] P. C. Clemmow & C. M. Munford, Philos. Trans. Roy. Soc. London Ser. A, v. 245, 1952, pp. 189-211. MR 14, 500. MR 0051574 (14:500e)
  • [13] K. A. Karpov, Tables of the Function $ w(z) = {e^{ - {z^2}}}\int {_0^z} {e^{x2}}dx$ in the Complex Domain, translated from the Russian, Pergamon Press, New York, 1965. MR 30 #4992. MR 0183096 (32:578)
  • [14] E. T. Goodwin, Proc. Cambridge Philos. Soc., v. 45, 1949, pp. 241-245. MR 10, 575. MR 0028938 (10:521b)
  • [15] M. Abramowitz & I. A. Stegun, (Editors), Handbook of Mathematical Functions, with Formulas, Graphs and Mathematical Tables, National Bureau of Standards, Applied Math. Series, No. 55, U. S. Government Printing Office, Washington, D. C., 1964. MR 29 #4914. MR 0167642 (29:4914)
  • [16] P. C. Rosenbloom & D. V. Widder, Trans. Amer. Math. Soc., v. 92, 1959, pp. 220-226. MR 21 #5845. MR 0107118 (21:5845)
  • [17] A. Reichel, J. Austral. Math. Soc., v. 4, 1964, pp. 476-488. MR 30 #4007. MR 0173799 (30:4007)
  • [18] C. Chiarella & A. Reichel, Monthly Notices Roy. Astronom. Soc., 134, pp. 83-86.
  • [19] Y. L. Luke, Integrals of Bessel Functions, McGraw-Hill, New York, 1962. MR 25 #5198. MR 0141801 (25:5198)

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DOI: https://doi.org/10.1090/S0025-5718-1968-0223068-4
Article copyright: © Copyright 1968 American Mathematical Society

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