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Miniaturized tables of Bessel functions. II


Author: Yudell L. Luke
Journal: Math. Comp. 25 (1971), 789-795
MSC: Primary 65A05
DOI: https://doi.org/10.1090/S0025-5718-1971-0298887-9
MathSciNet review: 0298887
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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/\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 [Enhancements On Off] (What's this?)

  • [1] Y. L. Luke, ``Miniaturized tables of Bessel functions,'' Math. Comp., v. 25, 1971, pp. 323-330. MR 0295508 (45:4574)
  • [2] 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.
  • [3] W. Gautschi, ``Computational aspects of three-term recurrence relations,'' SIAM Rev., v. 9, 1967, pp. 24-82. MR 35 #3927. MR 0213062 (35:3927)
  • [4] J. Wimp, Recent Developments in Recursive Computation, Aerospace Research Laboratories, Report ARL 69-0104, Wright-Patterson Air Force Base, Ohio, 1969. MR 0253554 (40:6768)
  • [5] Y. L. Luke, ``Evaluation of the Gamma function by means of Padé approximations,'' SIAM J. Math. Anal., v. 1, 1970, pp. 266-281. MR 0267141 (42:2043)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1971-0298887-9
Keywords: Bessel functions, approximation of bivariate functions, expansions in double series of Chebyshev polynomials, mathematical tables
Article copyright: © Copyright 1971 American Mathematical Society

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