A note on a problem in asymptotics
Author:
R. Shail
Journal:
Quart. Appl. Math. 58 (2000), 785-793
MSC:
Primary 78A30
DOI:
https://doi.org/10.1090/qam/1788428
MathSciNet review:
MR1788428
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Abstract: This note examines the asymptotic evaluation of two infinite series considered recently in [1] and [2], After a transformation to a more convenient form, elementary methods are used to derive extended asymptotic results (in one case the complete asymptotic expansion in the appropriate limit), and the numerical performance of the expansions is illustrated.
- 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
- Guido Dhondt, On the summation of a particular non-uniformly-convergent series, Quart. Appl. Math. 56 (1998), no. 1, 107–114. MR 1604809, DOI https://doi.org/10.1090/qam/1604809
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R. G. Cox and H. Brenner, The slow motion of a sphere through a viscous fluid towards a plane surface -II. Small gap widths including inertial effects, Chem. Engrg. Sci. 22, 1753-1777 (1967)
- R. Shail, On the asymptotic expansion of certain functions defined by infinite series, Mathematika 44 (1997), no. 2, 401–418. MR 1600498, DOI https://doi.org/10.1112/S0025579300012705
- Milton Van Dyke, Analysis and improvement of perturbation series, Quart. J. Mech. Appl. Math. 27 (1974), no. 4, 423–450. MR 468591, DOI https://doi.org/10.1093/qjmam/27.4.423
G. Dhondt and M. Köhl, On the force between a dielectric cylinder in a constant electric field and a conducting half space, Quart. Appl. Math. 55, 347-359 (1997)
G. Dhondt, On the summation of a particular non-uniformly-convergent series, Quart. Appl. Math. 56, 107-114 (1998)
A. D. Rawlins, Note on the capacitance of two closely separated spheres, IMA J. Applied Math. 34, 119-120 (1985)
R. G. Cox and H. Brenner, The slow motion of a sphere through a viscous fluid towards a plane surface -II. Small gap widths including inertial effects, Chem. Engrg. Sci. 22, 1753-1777 (1967)
R. Shail, On the asymptotic expansion of certain functions defined by infinite series, Mathematika 44, 401-418 (1997)
M. Van Dyke, Analysis and improvement of perturbation series, Quart. J. Mech. Appl. Math. 27, 423-450 (1974)
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Article copyright:
© Copyright 2000
American Mathematical Society
