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Miniaturized Tables of Bessel Functions, II

Yudell L. Luke
Mathematics of Computation
Vol. 25, No. 116 (Oct., 1971), pp. 789-795+s31-s57
DOI: 10.2307/2004345
Stable URL: http://www.jstor.org/stable/2004345
Page Count: 34
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Miniaturized Tables of Bessel Functions, II
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Abstract

In a previous study, we discussed the expansion of two-parameter functions in a double series of Chebyshev polynomials, and, in particular, we presented coefficients for the evaluation of the modified Bessel function (2z/π)1/2ezKν(z) to 20 decimals for all z ≥ 5 and all ν, 0 ≤ ν ≤ 1. In the present study, we give similar coefficients for the evaluation of ge-zzIν(z) to at least 20 decimals where Iν(z) is the modified Bessel function of the first kind and g and μ are certain constants which depend on the range of the parameter and variable for four different situations. The ranges are (1) $0 < z \leqq 8, 0 \leqq \nu \leqq 4$; (2) $0 < z \leqq 8, 4 \leqq \nu \leqq 8$; (3) z ≥ 8, -1 ≤ ν ≤ 0; (4); z ≥ 8, 0 ν ≤ 1.

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