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Rational Chebyshev approximations for the Bickley functions $ Ki\sb{n}(x)$


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
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Abstract: This report presents near-minimax rational approximations for the Bickley functions $ K{i_1}(x)$ for $ x \geqslant 0, K{i_2}(x)$ and $ K{i_3}(x)$ for $ 0 \leqslant x \leqslant 6$, and $ K{i_8}(x)$, $ K{i_9}(x)$ and $ K{i_{10}}(x)$ for $ x \geqslant 6$, with relative errors ranging down to $ {10^{ - 23}}$. The approximations, combined with the recurrence relation, yield a stable method of computing $ K{i_n}(x)$, $ n = 1,2, \ldots ,10$, for the complete range of the argument.


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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

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