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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
DOI: https://doi.org/10.1090/S0025-5718-1969-0247814-X
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. Gradšteŭ & I. M. Ryžik, Table of Integrals, Series, and Products, Fizmatgiz, Moscow, 1963; English transl., Academic Press, New York, 1965, pp. 369, 372. MR 28 #5198; MR 33 #5952. 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: https://doi.org/10.1090/S0025-5718-1969-0247814-X
Article copyright: © Copyright 1969 American Mathematical Society

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