Miniaturized tables of Bessel functions. II
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- by Yudell L. Luke PDF
- Math. Comp. 25 (1971), 789-795 Request permission
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 ${(2z/\pi )^{1/2}}{e^z}{K_v}(z)$ to 20 decimals for all $z \geqq 5$ and all $v,0 \leqq v \leqq 1$. In the present study, we give similar coefficients for the evaluation of $g{e^{ - z}}{z^{ - \mu }}{I_v}(z)$ to at least 20 decimals where ${I_v}(z)$ is the modified Bessel function of the first kind and g and $\mu$ are certain constants which depend on the range of the parameter and variable for four different situations. The ranges are $(1)\;0 < z \leqq 8,0 \leqq v \leqq 4;(2)\;0 < z \leqq 8,4 \leqq v \leqq 8;(3)\;z \geqq 8, - 1 \leqq v \leqq 0;(4)\;z \geqq 8,0 \leqq v \leqq 1$.References
- Yudell L. Luke, Miniaturized tables of Bessel functions, Math. Comp. 25 (1971), 323–330. MR 295508, DOI 10.1090/S0025-5718-1971-0295508-6 Y. L. Luke, The Special Functions and Their Approximations, Vols. I, II, Math. in Science and Engineering, vol. 53, Academic Press, New York, 1969. MR 39 #3039; MR 40 #2909.
- Walter Gautschi, Computational aspects of three-term recurrence relations, SIAM Rev. 9 (1967), 24–82. MR 213062, DOI 10.1137/1009002
- Jet Wimp, Derivative-free iteration processes of higher order, Aerospace Research Laboratories, Office of Aerospace Research, United States Air Force, Wright-Patterson Air Force Base, Ohio, 1969. ARL 69-0183. MR 0253554
- Yudell L. Luke, Evaluation of the gamma function by means of Padé approximations, SIAM J. Math. Anal. 1 (1970), 266–281. MR 267141, DOI 10.1137/0501024
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Math. Comp. 25 (1971), 789-795
- MSC: Primary 65A05
- DOI: https://doi.org/10.1090/S0025-5718-1971-0298887-9
- MathSciNet review: 0298887