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Expansion of Dawson’s function in a series of Chebyshev polynomials


Author: David G. Hummer
Journal: Math. Comp. 18 (1964), 317-319
MSC: Primary 65.25
DOI: https://doi.org/10.1090/S0025-5718-1964-0165687-6
MathSciNet review: 0165687
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    D. Harris III, “On the line-absorption coefficient due to Doppler effect and damping,” Astrophys. J., v. 108, 1948, p. 112-115. D. G. Hummer, “Noncoherent scattering. I. The redistribution functions with Doppler broadening,” Monthly Notices Roy. Astronom. Soc., v. 125, 1963, p. 21-37. W. L. Miller & A. R. Gordon, “Numerical evaluation of infinite series and integrals which arise in certain problems of linear heat flow, electrochemical diffusion, etc.,” J. Chem. Phys., v. 35, 1935, p. 2785-2884.
  • J. Barkley Rosser, Theory and Application of $\int _{0^z}e^{-x^{2}}dx$ and $\int _{0^z}e^{-p^{2}y^{2}}dy\int ^y_0 e^{-x^{2}}dx$. Part I. Methods of Computation, Mapleton House, Brooklyn, N. Y., 1948. MR 0027176
  • Bengt Lohmander and Stig Rittsten, Table of the function $y=e^{-x^{2}}\int ^{x} _{0}\,e^{t^{2}}dt$, Kungl. Fysiografiska Sällskapets i Lund Förhandlingar [Proc. Roy. Physiog. Soc. Lund] 28 (1958), 45–52. MR 94919
  • H. M. Terrill & L. Sweeny, “An extension of Dawson’s table of the integral of ${e^{{x^2}}}$,” J. Franklin Inst., v. 237, 1944, p. 495-497; “Table of the integral of ${e^{{x^2}}}$,” ibid., v. 238, 1944, p. 220-222.
  • Modern computing methods, Notes on Applied Science, No. 16, Her Majesty’s Stationery Office, London, 1961. 2nd ed; National Physical Laboratory. MR 0117863
  • C. W. Clenshaw, A note on the summation of Chebyshev series, Math. Tables Aids Comput. 9 (1955), 118–120. MR 71856, DOI https://doi.org/10.1090/S0025-5718-1955-0071856-0

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Article copyright: © Copyright 1964 American Mathematical Society