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 and be defined uniquely and be well-ordered in *n*. This is achieved by taking, for , . The necessary amendments to extant tables are indicated.

**[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