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Rational Chebyshev approximations for the Bessel functions $J_{0}(x)$, $J_{1}(x)$, $Y_{0}(x)$, $Y_{1}(x)$

Authors: C. A. Wills, J. M. Blair and P. L. Ragde
Journal: Math. Comp. 39 (1982), 617-623
MSC: Primary 65D20; Secondary 33A40, 41A50
MathSciNet review: 669653
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Abstract: This report presents near-minimax rational approximations for the Bessel functions ${J_0}(x)$, ${J_1}(x)$, ${Y_0}(x)$, and ${Y_1}(x)$ for the complete range of x, with relative errors ranging down to ${10^{ - 23}}$. The first thirty zeros of each function are listed to 35D. The tabulated zeros and the McMahon asymptotic formulae may be used to construct an algorithm which retains relative accuracy in the neighborhood of zeros.

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Keywords: Rational Chebyshev approximations, Bessel functions, McMahon expansions
Article copyright: © Copyright 1982 American Mathematical Society