Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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: 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.


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

  • [1] 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, https://doi.org/10.1090/qam/1447582
  • [2] 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
  • [3] M. D. Greenberg, Foundations of Applied Mathematics, Prentice-Hall Inc., Englewood Cliffs, N. J., 1978

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DOI: https://doi.org/10.1090/qam/1604809
Article copyright: © Copyright 1998 American Mathematical Society


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