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Note on the Kelvin phase functions


Author: J. R. Philip
Journal: Math. Comp. 33 (1979), 337-341
MSC: Primary 33A70
DOI: https://doi.org/10.1090/S0025-5718-1979-0514829-X
MathSciNet review: 514829
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Abstract: Both theoretical consistency and practical convenience demand that the values of the Kelvin phase functions $ {\theta _n}(x)$ and $ {\phi _n}(x)$ be defined uniquely and be well-ordered in n. This is achieved by taking, for $ n \geqslant 0$, $ {\theta _n}(0) = - {\phi _n}(0) = 3n\pi /4$. The necessary amendments to extant tables are indicated.


References [Enhancements On Off] (What's this?)

  • [1] N. W. McLACHLAN, Bessel Functions for Engineers, Clarendon Press, Oxford, 1934.
  • [2] A. YOUNG & A. KIRK, Bessel Functions, Part IV, Kelvin Functions, Roy. Soc. Math. Tables, vol. 10, University Press, Cambridge, 1964. MR 0164064 (29:1363)
  • [3] E. JAHNKE, F. EMDE, & F. LÖSCH, Tables of Higher Functions, 6th ed., McGraw-Hill, New York, 1960. MR 22 #5140.
  • [4] A. FLETCHER, J. C. P. MILLER, L. ROSENHEAD, & L. J. COMRIE, An Index of Mathematical Tables, 2nd ed., vol. I, Addison-Wesley, Reading, Mass., 1962. MR 26 #365a.
  • [5] F. W. J. OLVER, "9. Bessel functions of integer order," in M. Abramowitz & I. A. Stegun (Editors), Handbook of Mathematical Functions, Nat. Bur. Standards Appl. Math. Series 55, U. S. Dept. Commerce, Washington, D. C., 1964. MR 29 #4914.
  • [6] J. R. PHILIP, "Diurnal cycles in the lower atmosphere," Boundary Layer Meteorology. (To appear.)
  • [7] N. W. McLACHLAN & A. L. MEYERS, "The polar form of the ker and kei functions, with applications to eddy current heating," Philos. Mag. (7), v. 18, 1934, pp. 610-624.
  • [8] N. W. McLACHLAN, Bessel Functions for Engineers, 2nd ed., Clarendon Press, Oxford, 1955.
  • [9] F. F. D. BISACRE, "The calculation of the skin effect in electrical conductors," Philos. Mag. (6), v. 45, 1923, pp. 1026-1049.

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1979-0514829-X
Keywords: Kelvin phase functions
Article copyright: © Copyright 1979 American Mathematical Society

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