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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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  • [1] D. Harris III, ``On the line-absorption coefficient due to Doppler effect and damping,'' Astrophys. J., v. 108, 1948, p. 112-115.
  • [2] D. G. Hummer, ``Noncoherent scattering. I. The redistribution functions with Doppler broadening,'' Monthly Notices Roy. Astronom. Soc., v. 125, 1963, p. 21-37.
  • [3] 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.
  • [4] J. B. Rosser, Theory and Application of $ \int_0^\infty {{e^{ - {x^2}}}} dx$ and $ \int_0^z {{e^{ - {p^2}{y^2}}}dy\int_0^y {{e^{ - {x^2}}}} dx} $, Mapleton House, Brooklyn, N. Y., 1948. MR 0027176 (10:267e)
  • [5] B. Lohmander & S. Rittsten, ``Tables of the function $ y = {e^{ - {x^2}}}\int_0^x {{e^{{t^2}}}} dt$,'' Kungl. Fysiogr. Sällsk. i Lund Förh., v. 28, 1958, p. 45-52. MR 0094919 (20:1427)
  • [6] 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.
  • [7] National Physical Laboratory, Modern Computing Methods, 2nd edition, H. M. Stationery Office, London, 1961. MR 0117863 (22:8637)
  • [8] C. W. Clenshaw, ``A note on the summation of Chebyshev series,'' MTAC, v. 9, 1955, p. 118-120; see also [7], Chapter 8. MR 0071856 (17:194e)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1964-0165687-6
Article copyright: © Copyright 1964 American Mathematical Society

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