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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Summation of a slowly convergent series arising in antenna study


Author: Chi Fu Den
Journal: Math. Comp. 23 (1969), 651-654
MSC: Primary 78.65
MathSciNet review: 0247814
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Abstract: An equivalent series for the slowly convergent series

$\displaystyle \sum\limits_{n = 1}^\infty {\left[ {\smallint _{ - \pi /2}^{\pi /2}{{\cos }^\alpha }\theta \cos (n \in \sin \theta )} \right]} {}^2/n$

which arises in antenna theory is obtained. The new form is found to consist of two rapidly convergent series for small $ \in $.

References [Enhancements On Off] (What's this?)

  • [1] C. F. Den, Admittance of a Wedge Excited Co-axial Antenna with a Plasma Sheath, Technical Report 5825-9-T, University of Michigan, Radiation Laboratory, Ann Arbor, Mich., 1966.
  • [2] I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, Fourth edition prepared by Ju. V. Geronimus and M. Ju. Ceĭtlin. Translated from the Russian by Scripta Technica, Inc. Translation edited by Alan Jeffrey, Academic Press, New York-London, 1965. MR 0197789 (33 #5952)
  • [3] P. J. B. Clarricoats & A. A. Oliner, "Improved theory of propagation through slotted circular waveguide," Eledronics Letters, v. 3, 1967, pp. 279-282.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1969-0247814-X
PII: S 0025-5718(1969)0247814-X
Article copyright: © Copyright 1969 American Mathematical Society