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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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Rational Chebyshev approximations for the modified Bessel functions $I_{0}(x)$ and $I_{1}(x)$
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by J. M. Blair PDF
Math. Comp. 28 (1974), 581-583 Request permission

Abstract:

This note presents nearly-best rational approximations for the functions ${I_0}(x)$ and ${I_1}(x)$, with relative errors ranging down to ${10^{ - 23}}$.
References
    Y. L. Luke, The Special Functions and Their Approximations. Vol. 2, Math. in Science and Engineering, vol. 53, Academic Press, New York, 1969. MR 40 #2909.
  • C. W. Clenshaw, Chebyshev series for mathematical functions, National Physical Laboratory Mathematical Tables, Vol. 5, Her Majesty’s Stationery Office, London, 1962. Department of Scientific and Industrial Research. MR 0142793
  • Jet Wimp, Polynomial expansions of Bessel functions and some associated functions, Math. Comp. 16 (1962), 446–458. MR 148956, DOI 10.1090/S0025-5718-1962-0148956-3
  • I. Gargantini, "On the application of the process of equalization of maxima to obtain rational approximations to certain modified Bessel functions," Comm. ACM, v. 9, 1966, pp. 859-863. A. E. Russon & J. M. Blair, Rational Function Minimax Approximations for the Bessel Functions ${K_0}(x)$ and ${K_1}(x)$, Report AECL-3461, Atomic Energy of Canada Limited, Chalk River, Ontario, 1969. J. F. Hart et al., Computer Approximations, Wiley, New York, 1968. J. H. Johnson & J. M. Blair, REMES 2—A FORTRAN Program to Calculate Rational Minimax Approximations to a Given Function, Report AECL-4210, Atomic Energy of Canada Limited, Chalk River, Ontario, 1973. B. S. Berger & H. McAllister, "A table of the modified Bessel functions ${K_n}(x)$ and ${I_n}(x)$ to at least 60S for $n = 0,1$ and $x = 1,2, \cdots ,40,$" Math. Comp., v. 24, 1970, p. 488, RMT 34.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Math. Comp. 28 (1974), 581-583
  • MSC: Primary 65D20
  • DOI: https://doi.org/10.1090/S0025-5718-1974-0341810-1
  • MathSciNet review: 0341810