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Rational Chebyshev Approximations for the Bessel Functions $J_0(x), J_1(x), Y_0(x), Y_1(x)$

C. A. Wills, J. M. Blair and P. L. Ragde
Mathematics of Computation
Vol. 39, No. 160 (Oct., 1982), pp. 617-623
DOI: 10.2307/2007338
Stable URL: http://www.jstor.org/stable/2007338
Page Count: 67
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Rational Chebyshev Approximations for the Bessel Functions $J_0(x), J_1(x), Y_0(x), Y_1(x)$
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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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