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Magnetic Decay in a Hollow Elliptic Cylinder. II
1.M. A. Weinstein, J. Appl. Phys. 37, 248 (1966).
2.We use the notation of Tables Relating to Mathieu Functions (Columbia University Press, New York, 1951).
3.N. F. McLachlan, Theory and Application of Mathieu Functions (Oxford University Press, London, 1947).
4.P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw‐Hill Book Company, New York, 1953).
5.Except when in which case See Eqs. (11) and (16).
6.H. Jeffreys, Asymptotic Approximations (Oxford University Press, London, 1962).
7.See Eq. (16).
8.This result can also be obtained by expanding the modified Mathieu functions in Eq. (2) in powers of and and retaining only the dominant terms in s in the coefficients of a given order in and
9.Ref. 3, p. 210.
10.It is readily shown that the series in Eq. (17) converges for
11.A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Tables of Integral Transforms (McGraw‐Hill Book Company, New York, 1954), Vol. 1.
12.If the condition is not satisfied, the term in in the bracket of Eq. (28) should not be retained. A better approximation is then given by Eq. (22) of Ref. 1.
13.It should be noted that direct numerical solution of Eq. (2) for large s is not feasible because the number of terms which contribute significantly to the sum increases rapidly with s.
14.S. D. Daymond, Quart. J. Mech. Appl. Math. 8, 361 (1955).
15.Ref. 1, Table II.
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