Rational Chebyshev approximations for the Bickley functions
Authors:
J. M. Blair, C. A. Edwards and J. H. Johnson
Journal:
Math. Comp. 32 (1978), 876886
MSC:
Primary 65D20
Corrigendum:
Math. Comp. 38 (1982), 657.
MathSciNet review:
0471262
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Abstract 
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Abstract: This report presents nearminimax 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.
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 W. G. BICKLEY, "Some solutions of the problem of forced convection," Philos. Mag., v. 20, 1935, pp. 322343.
 [2]
 W. G. BICKLEY & J. NAYLER, "A short table of the functions , from to ," Philos. Mag., v. 20, 1935, pp. 343347.
 [3]
 Y. L. LUKE, Integrals of Bessel Functions, McGrawHill, 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. 8284.
 [6]
 I. GARGANTINI & T. POMENTALE, "Rational Chebyshev approximations to the Bessel function integrals ," Comm. ACM, v. 7, 1964, pp. 727730. MR 0176591 (31:863)
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 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.
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 K. MAKINO, "Some rational approximations for the Bickley functions ," Nukleonik, v. 9, 1967, pp. 351352.
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 Y. L. LUKE, Mathematical Functions and Their Approximations, Academic Press, New York, 1975. MR 0501762 (58:19039)
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 W. J. CODY, "A survey of practical rational and polynomial approximation of functions," SIAM Rev., v. 12, 1970, pp. 400423. MR 0267725 (42:2627)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197804712626
PII:
S 00255718(1978)04712626
Keywords:
Rational Chebyshev approximations,
Bickley functions,
Bessel function integrals
Article copyright:
© Copyright 1978
American Mathematical Society
