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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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
MathSciNet review: 0120401
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  • [1] E. Dempsey and G. C. Benson, Tables of the modified Bessel functions of the second kind for particular types of argument, Canad. J. Phys. 38 (1960), 399–424. MR 0110226 (22 #1106)
  • [2] R. B. Dingle, Asymptotic expansions and converging factors. I. General theory and basic converging factors, Proc. Roy. Soc. London. Ser. A 244 (1958), 456–475. 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. Ser. A 249 (1959), 270–283. 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] Eugene Jahnke and Fritz Emde, Tables of Functions with Formulae and Curves, Dover Publications, New York, N. Y., 1945. 4th ed. 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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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1960-0120401-1
PII: S 0025-5718(1960)0120401-1
Article copyright: © Copyright 1960 American Mathematical Society