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Note on the asymptotic expansion of the modified Bessel function of the second kind


Authors: E. Dempsey and G. C. Benson
Journal: Math. Comp. 14 (1960), 362-365
MSC: Primary 33.00
DOI: https://doi.org/10.1090/S0025-5718-1960-0120401-1
MathSciNet review: 0120401
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  • [1] E. Dempsey & G. C. Benson, ``Tables of the modified Bessel functions of the second kind for particular types of argument,'' Can Jn. Phys., v. 38, 1960, p. 399. This paper contains tables of $ {K_n}\left({\tfrac{\pi }{2}\sqrt q }\right)$ for q = 1(1.0) 250 and of $ {K_n}\left({\tfrac{\pi }{3}\sqrt q }\right)$ for q = 1(1.0) 300. In both cases values for integral orders 0 to 10 were computed to ten significant figures. MR 0110226 (22:1106)
  • [2] R. B. Dingle, ``Asymptotic expansions and converging factors. I. General theory and basic converging factors,'' Proc., Roy. Soc., London, v. 244A, 1958, p. 456. MR 0103373 (21:2145)
  • [3] R. B. Dingle, ``Asymptotic expansions and converging factors. IV Confluent hypergeometric, parabolic cylinder, modified Bessel, and ordinary Bessel functions,'' Proc., Roy. Soc., London, v. 249A, 1959, p. 270. MR 0103376 (21:2148a)
  • [4] D. Burnett, ``The remainders in the asymptotic expansions of certain Bessel functions,'' Proc., Camb. Phil. Soc., v. 26, 1930, p. 145.
  • [5] E. Jahnke & F. Emde, Tables of Functions, Fourth Edition, Dover, New York, 1945, p. 138. MR 0015900 (7:485b)
  • [6] W. S. Aldis, ``Tables for the solution of the equation $ \tfrac{{{d^2}y}}{{d{x^2}}} + \tfrac{1}{x} \cdot \tfrac{{dy}}{{dx}} - \left({1 + \tfrac{{{n^2}}}{{{x^2}}}}\right)y = 0$,'' proc., Roy. Soc., London, v. 64, 1899, p. 203.

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DOI: https://doi.org/10.1090/S0025-5718-1960-0120401-1
Article copyright: © Copyright 1960 American Mathematical Society

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