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Mathematics of Computation

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Miniaturized tables of Bessel functions. III


Author: Yudell L. Luke
Journal: Math. Comp. 26 (1972), 237-240
MSC: Primary 65A05
DOI: https://doi.org/10.1090/S0025-5718-1972-0298888-1
MathSciNet review: 0298888
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Abstract: 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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Keywords: Bessel functions, approximation of bivariate functions, expansions in double series of Chebyshev polynomials, mathematical tables
Article copyright: © Copyright 1972 American Mathematical Society