Summation of a slowly convergent series arising in antenna study
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- by Chi Fu Den PDF
- Math. Comp. 23 (1969), 651-654 Request permission
Abstract:
An equivalent series for the slowly convergent series \[ \sum \limits _{n = 1}^\infty {\left [ {\smallint _{ - \pi /2}^{\pi /2}{{\cos }^\alpha }\theta \cos (n \in \sin \theta )} \right ]} {}^2/n\] which arises in antenna theory is obtained. The new form is found to consist of two rapidly convergent series for small $\in$.References
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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.
- I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, Academic Press, New York-London, 1965. Fourth edition prepared by Ju. V. Geronimus and M. Ju. Ceĭtlin; Translated from the Russian by Scripta Technica, Inc; Translation edited by Alan Jeffrey. MR 0197789 P. J. B. Clarricoats & A. A. Oliner, "Improved theory of propagation through slotted circular waveguide," Eledronics Letters, v. 3, 1967, pp. 279–282.
Additional Information
- © Copyright 1969 American Mathematical Society
- 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