Note on the Kelvin phase functions
Author:
J. R. Philip
Journal:
Math. Comp. 33 (1979), 337341
MSC:
Primary 33A70
DOI:
https://doi.org/10.1090/S0025571819790514829X
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 wellordered 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.

N. W. McLACHLAN, Bessel Functions for Engineers, Clarendon Press, Oxford, 1934.
 Bessel functions. Part IV: Kelvin functions, Royal Society Mathematical Tables, Vol. 10, Published for the Royal Society at the Cambridge University Press, New York, 1964. Prepared on behalf of The Mathematical Tables Committee by Andrew Young and Alan Kirk. MR 0164064 E. JAHNKE, F. EMDE, & F. LÖSCH, Tables of Higher Functions, 6th ed., McGrawHill, New York, 1960. MR 22 #5140. A. FLETCHER, J. C. P. MILLER, L. ROSENHEAD, & L. J. COMRIE, An Index of Mathematical Tables, 2nd ed., vol. I, AddisonWesley, Reading, Mass., 1962. MR 26 #365a. 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. J. R. PHILIP, "Diurnal cycles in the lower atmosphere," Boundary Layer Meteorology. (To appear.) 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. 610624. N. W. McLACHLAN, Bessel Functions for Engineers, 2nd ed., Clarendon Press, Oxford, 1955. F. F. D. BISACRE, "The calculation of the skin effect in electrical conductors," Philos. Mag. (6), v. 45, 1923, pp. 10261049.
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Keywords:
Kelvin phase functions
Article copyright:
© Copyright 1979
American Mathematical Society