Rational Chebyshev approximations for the modified Bessel functions $I_{0}(x)$ and $I_{1}(x)$
Author:
J. M. Blair
Journal:
Math. Comp. 28 (1974), 581583
MSC:
Primary 65D20
DOI:
https://doi.org/10.1090/S00255718197403418101
MathSciNet review:
0341810
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Abstract  References  Similar Articles  Additional Information
Abstract: This note presents nearlybest rational approximations for the functions ${I_0}(x)$ and ${I_1}(x)$, with relative errors ranging down to ${10^{  23}}$.

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.
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 Jet Wimp, Polynomial expansions of Bessel functions and some associated functions, Math. Comp. 16 (1962), 446–458. MR 148956, DOI https://doi.org/10.1090/S00255718196201489563 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. 859863. A. E. Russon & J. M. Blair, Rational Function Minimax Approximations for the Bessel Functions ${K_0}(x)$ and ${K_1}(x)$, Report AECL3461, 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 AECL4210, 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
Keywords:
Rational Chebyshev approximations,
Bessel functions
Article copyright:
© Copyright 1974
American Mathematical Society