Toroidal wave functions
Author:
V. H. Weston
Journal:
Quart. Appl. Math. 16 (1958), 237-257
MSC:
Primary 33.00; Secondary 35.00
DOI:
https://doi.org/10.1090/qam/104001
MathSciNet review:
104001
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Abstract: The Helmholtz equation is solved in toroidal coordinates. A complete set of solutions is obtained representing radiations from a ring source.
A. Erdelyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher transcendental functions, vol. I, New York, 1953.
E. W. Hobson, The theory of spherical and ellipsoidal harmonics, Cambridge, 1931
- Arthur Erdélyi, Wilhelm Magnus, Fritz Oberhettinger, and Francesco G. Tricomi, Higher transcendental functions. Vol. III, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. Based, in part, on notes left by Harry Bateman. MR 0066496
J. Stratton, Electromagnetic theory, McGraw-Hill, 1941.
W. Magnus and F. Oberhettinger, Functions of mathematical Physics, (English ed. 1949)
V. H. Weston, Solutions of the toroidal wave equation and their applications, Ph.D. thesis, University of Toronto, 1956
- Vaughan H. Weston, Solutions of the Helmholtz equation for a class of non-separable cylindrical and rotational coordinate systems, Quart. Appl. Math. 15 (1958), 420–427. MR 98238, DOI https://doi.org/10.1090/S0033-569X-1958-98238-5
A. Erdelyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher transcendental functions, vol. I, New York, 1953.
E. W. Hobson, The theory of spherical and ellipsoidal harmonics, Cambridge, 1931
A. Erdelyi, W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher transcendental functions, vol. II, New York, 1954.
J. Stratton, Electromagnetic theory, McGraw-Hill, 1941.
W. Magnus and F. Oberhettinger, Functions of mathematical Physics, (English ed. 1949)
V. H. Weston, Solutions of the toroidal wave equation and their applications, Ph.D. thesis, University of Toronto, 1956
V. H. Weston, Solutions of the Helmholtz equation for a class of non-separable cylindrical and Rotational coordinate systems, Quart. Appl. Math. 15, 420 (1957)
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Article copyright:
© Copyright 1958
American Mathematical Society
