Note on the Kelvin phase functions
Author:
J. R. Philip
Journal:
Math. Comp. 33 (1979), 337341
MSC:
Primary 33A70
MathSciNet review:
514829
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: Both theoretical consistency and practical convenience demand that the values of the Kelvin phase functions and be defined uniquely and be wellordered 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]
Bessel functions. Part IV: Kelvin functions, Prepared on behalf
of The Mathematical Tables Committee by Andrew Young and Alan Kirk. Royal
Society Mathematical Tables, Vol. 10, Published for the Royal Society at
the Cambridge University Press, New York, 1964. MR 0164064
(29 #1363)
 [3]
E. JAHNKE, F. EMDE, & F. LÖSCH, Tables of Higher Functions, 6th ed., McGrawHill, 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, AddisonWesley, 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. 610624.
 [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. 10261049.
 [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., McGrawHill, 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, AddisonWesley, 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. 610624.
 [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. 10261049.
Similar Articles
Retrieve articles in Mathematics of Computation
with MSC:
33A70
Retrieve articles in all journals
with MSC:
33A70
Additional Information
DOI:
http://dx.doi.org/10.1090/S0025571819790514829X
PII:
S 00255718(1979)0514829X
Keywords:
Kelvin phase functions
Article copyright:
© Copyright 1979
American Mathematical Society
