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The analyticity of cross-product Bessel function zeros

Published online by Cambridge University Press:  24 October 2008

James Alan Cochran
James Alan Cochran
Affiliation:
Bell Telephone Laboratories, Incorporated, Whippany, New Jersey
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Extract

Introduction. In this paper we consider the two cross-product combinations of Bessel functions

where δ = (k − 1) z and (') denotes differentiation with respect to the argument. Here Jν and Yν designate respectively the Bessel functions of the first and second kind of order ν.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 2 , April 1966 , pp. 215 - 226
Copyright
Copyright © Cambridge Philosophical Society 1966

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References

REFERENCES

(1)McMahon, J.Ann. of Math. 9 (1894), 23–30.CrossRefGoogle Scholar
(2)Cochran, J. A. (to appear).Google Scholar
(3)Gray, A. and Mathews, G. B.Bessel functions (MacMillan; London, 1922), 82.Google Scholar
(4)Buchholz, H.Elek. Nachrichtentech. 16 (1939), 73–85.Google Scholar
(5)Buchholz, H.Z. Angew. Math. Mech. 29 (1949), 356–367.Google Scholar
(6)Truell, R.J. Appl. Phys. 14 (1943), 350–352.Google Scholar
(7)Kline, M.J. Math. Phys. 27 (1948), 37–48.Google Scholar
(8)Gunston, M. A. R.IEEE Trans. Microw. Theor. Tech. MTT-11 (1963), 93–94.Google Scholar
(9)Cochran, J. A.IEEE Trans. Microw. Theor. Tech. MTT-11 (1963), 546–547.Google Scholar
(10)Cochran, J. A.J. Soc. Indust. Appl. Math. 12 (1964), 580–587.CrossRefGoogle Scholar
(11)Willis, D. M.Proc. Cambridge Philos. Soc. 61 (1965), 425–428.CrossRefGoogle Scholar
(12)Fletcher, A., Miller, J. C. P., Rosenhead, L. and Comrie, L. J.An index of mathe matical tables, vol. 1 (Scientific Computing Service; London, 1962).Google Scholar
(13)Waldron, R. A.J. Brit. Inst. Radio Eng. 17 (1947), 577–592.Google Scholar
(14)Bridge, J. F. and Angrist, S. W.Math. Comp 16 (1962), 198–204.Google Scholar
(15)Laslett, L. J. and Lewish, W.Math. Comp. 16 (1962), 226–232.CrossRefGoogle Scholar
(16)Bauer, H. F.Math. Comp. 18 (1964), 128–135.Google Scholar
(17)Watson, G. N.A treatise on the theory of Bessel functions (2nd ed.; Cambridge, 1958).Google Scholar
(18)Abramowitz, M. and Stegun, I. A., editors. Handbook of mathematical functions with formulas, graphs, and mathematical tables, Appl. Math. Series 55 (U.S. National Bureau of Standards; Washington, D. C, 1964), 362.Google Scholar
(19)Hille, E.Analytic function theory, vol. 1, 269–275. (Ginn; Boston, 1959.)Google Scholar