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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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Miniaturized tables of Bessel functions. III
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by Yudell L. Luke PDF
Math. Comp. 26 (1972), 237-240 Request permission


After the manner of our previous studies, coefficients for the expansion of ${J_\nu }(z)$ and ${Y_\nu }(z)$ in double series of Chebyshev polynomials are presented. For ${J_\nu }(z)$ the ranges are (1) $0 < z \leqq 8,0 \leqq \nu \leqq 4$, (2) $0 < z \leqq 8,4 \leqq \nu \leqq 8$. For ${J_\nu }(z) + i{Y_\nu }(z)$, the ranges are $z \geqq 5$ and $0 \leqq \nu \leqq 1$. The coefficients are given with sufficient accuracy to enable the evaluation of the Bessel functions to at least 20 decimals.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Math. Comp. 26 (1972), 237-240
  • MSC: Primary 65A05
  • DOI:
  • MathSciNet review: 0298888