Rational Chebyshev approximations for the modified Bessel functions and

Author:
J. M. Blair

Journal:
Math. Comp. **28** (1974), 581-583

MSC:
Primary 65D20

DOI:
https://doi.org/10.1090/S0025-5718-1974-0341810-1

MathSciNet review:
0341810

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Abstract | References | Similar Articles | Additional Information

Abstract: This note presents nearly-best rational approximations for the functions and , with relative errors ranging down to .

**[1]**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.**[2]**C. W. Clenshaw,*Chebyshev Series for Mathematical Functions*, Nat. Phys. Lab. Math. Tables, vol. 5, Her Majesty's Stationery Office, London, 1962. MR**26**#362. MR**0142793 (26:362)****[3]**J. Wimp, "Polynomial expansions of Bessel functions and some associated functions,"*Math. Comp.*, v. 16, 1962, pp. 446-458. MR**26**#6452. MR**0148956 (26:6452)****[4]**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.**[5]**A. E. Russon & J. M. Blair,*Rational Function Minimax Approximations for the Bessel Functions**and*, Report AECL-3461, Atomic Energy of Canada Limited, Chalk River, Ontario, 1969.**[6]**J. F. Hart et al.,*Computer Approximations*, Wiley, New York, 1968.**[7]**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.**[8]**B. S. Berger & H. McAllister, "A table of the modified Bessel functions and to at least 60S for and "*Math. Comp.*, v. 24, 1970, p. 488, RMT 34.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1974-0341810-1

Keywords:
Rational Chebyshev approximations,
Bessel functions

Article copyright:
© Copyright 1974
American Mathematical Society