Rational Chebyshev approximations for the Bickley functions

Authors:
J. M. Blair, C. A. Edwards and J. H. Johnson

Journal:
Math. Comp. **32** (1978), 876-886

MSC:
Primary 65D20

DOI:
https://doi.org/10.1090/S0025-5718-1978-0471262-6

Corrigendum:
Math. Comp. **38** (1982), 657.

MathSciNet review:
0471262

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This report presents near-minimax rational approximations for the Bickley functions for and for , and , and for , with relative errors ranging down to . The approximations, combined with the recurrence relation, yield a stable method of computing , , for the complete range of the argument.

**[1]**W. G. BICKLEY, "Some solutions of the problem of forced convection,"*Philos. Mag.*, v. 20, 1935, pp. 322-343.**[2]**W. G. BICKLEY & J. NAYLER, "A short table of the functions , from to ,"*Philos. Mag.*, v. 20, 1935, pp. 343-347.**[3]**Y. L. LUKE,*Integrals of Bessel Functions*, McGraw-Hill, New York, 1962. MR**0141801 (25:5198)****[4]**D. DAVIERWALLA,*Tschebyscheff Rational Approximations to Bickley Functions*, EIR Report No. 243, 1973.**[5]**A. J. CLAYTON, "Some rational approximations for the and functions,"*J. Nuclear Energy*, Parts A/B, v. 18, 1964, pp. 82-84.**[6]**I. GARGANTINI & T. POMENTALE, "Rational Chebyshev approximations to the Bessel function integrals ,"*Comm. ACM*, v. 7, 1964, pp. 727-730. MR**0176591 (31:863)****[7]**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.**[8]**K. MAKINO, "Some rational approximations for the Bickley functions ,"*Nukleonik*, v. 9, 1967, pp. 351-352.**[9]**Y. L. LUKE,*Mathematical Functions and Their Approximations*, Academic Press, New York, 1975. MR**0501762 (58:19039)****[10]**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.**[11]**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**.**[12]**J. F. HART, et al.,*Computer Approximations*, Wiley, New York, 1968.**[13]**C. MESZTENYI & C. WITZGALL, "Stable evaluation of polynomials,"*J. Res. Nat. Bur. Standards Sect. B*, v. 71B, 1967, pp. 11-17. MR**0212994 (35:3859)****[14]**W. J. CODY, "A survey of practical rational and polynomial approximation of functions,"*SIAM Rev.*, v. 12, 1970, pp. 400-423. MR**0267725 (42:2627)**

Retrieve articles in *Mathematics of Computation*
with MSC:
65D20

Retrieve articles in all journals with MSC: 65D20

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1978-0471262-6

Keywords:
Rational Chebyshev approximations,
Bickley functions,
Bessel function integrals

Article copyright:
© Copyright 1978
American Mathematical Society