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Online ISSN 1552-4485; Print ISSN 0033-569X
On the summation of a particular non-uniformly-convergent series
Author:
Guido Dhondt
Journal:
Quart. Appl. Math. 56 (1998), 107-114
MSC:
Primary 40A30
DOI:
https://doi.org/10.1090/qam/1604809
MathSciNet review:
MR1604809
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Abstract | References | Similar Articles | Additional Information
Abstract: In a previous article the force between a dielectric cylinder and a conducting half-space for the cylinder approaching the half-space was obtained as the limit of a non-uniformly-convergent series. A special asymptotic analysis was performed to get a closed-form solution for this limit. The present article focuses on a delicate and crucial step in this analysis and gives a justification by a mathematically rigorous proof.
- Guido Dhondt and Manfred Köhl, On the force between a dielectric cylinder in a constant electric field and a conducting half space, Quart. Appl. Math. 55 (1997), no. 2, 347–359. MR 1447582, DOI https://doi.org/10.1090/qam/1447582
- I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, 6th ed., Academic Press, Inc., San Diego, CA, 2000. Translated from the Russian; Translation edited and with a preface by Alan Jeffrey and Daniel Zwillinger. MR 1773820 M. D. Greenberg, Foundations of Applied Mathematics, Prentice-Hall Inc., Englewood Cliffs, N. J., 1978
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Article copyright:
© Copyright 1998
American Mathematical Society