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Mathematics of Computation

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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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by C. A. Wills, J. M. Blair and P. L. Ragde PDF
Math. Comp. 39 (1982), 617-623 Request permission


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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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Math. Comp. 39 (1982), 617-623
  • MSC: Primary 65D20; Secondary 33A40, 41A50
  • DOI:
  • MathSciNet review: 669653