Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Simplified calculation of $ \mathrm{Ei}(x)$ for positive arguments, and a short table of $ \mathrm{Shi}(x)$


Authors: Robert F. Tooper and John Mark
Journal: Math. Comp. 22 (1968), 448-449
DOI: https://doi.org/10.1090/S0025-5718-68-99872-4
Full-text PDF

References | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] C. W. Clenshaw, Chebyshev Series for Mathematical Functions, National Physical Laboratory Mathematical Tables, Vol. 5, H. M. S. O., London, 1962, p. 29. MR 26 #362.
  • [2] C. W. Clenshaw, G. F. Miller & M. Woodger, "Algorithms for special functions. I," Numer. Math., v. 4, 1963, pp. 403-419. MR 27 #4346. MR 0154397 (27:4346)
  • [3] W. J. Cody & J. Stoer, "Rational Chebyshev approximation using interpolation," Numer. Math., v. 9, 1966, pp. 177-188.
  • [4] P. J. Davis & I. Polonsky, "Numerical interpolation, differentiation and integration," Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun, National Bureau of Standards Appl. Math. Series, No. 55, U. S. Government Printing Office, Washington, D. C., 1964, p. 917.
  • [5] F. E. Harris, "Tables of the exponential integral $ Ei(x)$," MTAC, v. 11, 1957, pp. 9-16. MR 19, 464. MR 0088069 (19:464b)
  • [6] M. Kotani, A. Amemiya, E. Ishiguro & T. Kimura, Table of Molecular Integrals, Maruzen, Tokyo, 1955. MR 19, 324. MR 0087231 (19:324f)
  • [7] J. Miller & R. P. Hurst, "Simplified calculation of the exponential integral," MTAC, v. 12, 1958, pp. 187-193. MR 21 #3103. MR 0104348 (21:3103)
  • [8] A. Ralston, A First Course in Numerical Analysis, McGraw-Hill, New York, 1965, pp. 301-306. MR 32 #8479. MR 0191070 (32:8479)
  • [9] D. van Z. Wadsworth, "Improved asymptotic expansion for the exponential integral with positive argument," Math. Comp., v. 19, 1965, pp. 327-328.


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-68-99872-4
Article copyright: © Copyright 1968 American Mathematical Society

American Mathematical Society