Rational Chebyshev approximations for the exponential integral
Authors:
W. J. Cody and Henry C. Thacher
Journal:
Math. Comp. 22 (1968), 641649
MSC:
Primary 65.25
MathSciNet review:
0226823
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: Rational Chebyshev approximations are presented for the exponential integral in the intervals , , and with maximal relative errors ranging down to . coefficients are also given for a continuedfraction expansion for small .
 [1]
Handbook of mathematical functions, with formulas, graphs, and
mathematical tables, Edited by Milton Abramowitz and Irene A. Stegun.
Third printing, with corrections. National Bureau of Standards Applied
Mathematics Series, vol. 55, Superintendent of Documents, U.S.
Government Printing Office, Washington, D.C., 1965. MR 0177136
(31 #1400)
 [2]
E. E. Allen, ``Note 169,'' MTAC, v. 8, 1954, p. 240.
 [3]
Cecil
Hastings Jr., Approximations for digital computers, Princeton
University Press, Princeton, N. J., 1955. Assisted by Jeanne T. Hayward and
James P. Wong, Jr. MR 0068915
(16,963e)
 [4]
C. Hastings, Jr., ``Note 143,'' MTAC, v. 7, 1953, p. 68.
 [5]
C. W. Clenshaw, Chebyshev Series for Mathematical Functions, National Physical Laboratorv Math. Tables, Vol. 5, Department of Scientific and Industrial Research, H.M.S.O., London, 1962. MR 26 #362.
 [6]
W. Fraser & J. F. Hart, ``On the computation of rational approximations to continuous functions,'' Comm. ACM, v. 5, 1962, pp. 401403.
 [7]
W. J. Cody & J. Stoer, ``Rational Chebyshev approximations using interpolation,'' Numer. Math., v. 9, 1966, pp. 177188.
 [8]
Peter
Henrici, Some applications of the quotientdifference
algorithm, Proc. Sympos. Appl. Math., Vol. XV, Amer. Math. Soc.,
Providence, R.I., 1963, pp. 159–183. MR 0159415
(28 #2632)
 [1]
 W. Gautschi & W. F. Cahill, ``Exponential integral and related functions,'' Chapter 5 in Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, edited by M. Abramowitz &I. A. Stegun, Nat. Bur. Standards Appl. Math. Series, 55, Superintendent of Documents, U. S. Government Printing Office, Washington, D. C., 1964; 3rd printing, with corrections, 1965. MR 29 #4914; MR 31 #1400. MR 0177136 (31:1400)
 [2]
 E. E. Allen, ``Note 169,'' MTAC, v. 8, 1954, p. 240.
 [3]
 C. Hastings, Jr., Approximations for Digital Computers, Princeton Univ. Press, Princeton, N. J., 1955, pp. 188190. MR 16, 963. MR 0068915 (16:963e)
 [4]
 C. Hastings, Jr., ``Note 143,'' MTAC, v. 7, 1953, p. 68.
 [5]
 C. W. Clenshaw, Chebyshev Series for Mathematical Functions, National Physical Laboratorv Math. Tables, Vol. 5, Department of Scientific and Industrial Research, H.M.S.O., London, 1962. MR 26 #362.
 [6]
 W. Fraser & J. F. Hart, ``On the computation of rational approximations to continuous functions,'' Comm. ACM, v. 5, 1962, pp. 401403.
 [7]
 W. J. Cody & J. Stoer, ``Rational Chebyshev approximations using interpolation,'' Numer. Math., v. 9, 1966, pp. 177188.
 [8]
 P. Henrici, ``Some applications of the quotient difference algorithm'' in High Speed Computing and Experimental Arithmetic, Proc. Sympos. Appl. Math., Vol. 15, Amer. Math. Soc., Providence, R. I., 1963, pp. 159183. MR 28 #2632. MR 0159415 (28:2632)
Similar Articles
Retrieve articles in Mathematics of Computation
with MSC:
65.25
Retrieve articles in all journals
with MSC:
65.25
Additional Information
DOI:
http://dx.doi.org/10.1090/S0025571819680226823X
PII:
S 00255718(1968)0226823X
Article copyright:
© Copyright 1968 American Mathematical Society
