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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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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