On the highly accurate summation of certain series occurring in plate contact problems
Author:
D. A. MacDonald
Journal:
Math. Comp. 66 (1997), 1619-1627
MSC (1991):
Primary 65B10; Secondary 35Q80, 35J25
DOI:
https://doi.org/10.1090/S0025-5718-97-00869-7
MathSciNet review:
1423078
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Abstract | References | Similar Articles | Additional Information
Abstract: The infinite series and the related series
are of interest in problems concerning contact between plates and unilateral supports. This article will re-examine a previously published result of Baratella and Gabutti for , and will present new, rapidly convergent, series for
and
- 1. M. Abramowitz and I.A. Stegun, Handbook of mathematical functions, Dover Publications Inc., New York, (1966). MR 34:8606
- 2. P. Baratella and B. Gabutti, Uniform approximation on unit disk of series arising in plate contact problems, Jl of Comp. & Appl. Math. 62 (1995) 181-196. MR 96h:65003
- 3. J. Boersma and J.P. Dempsey, Numerical evaluation of Legendre's Chi-function, Math. Comp. 59 (1992) 157-163. MR 92k:65008
- 4. J.P. Dempsey , L.M. Keer, N.B. Patel and M.L. Glasser, Contact between plates and unilateral supports, ASME J Appl. Mech 51 (1984) 324-328.
- 5.
K.M. Dempsey, D Liu, and J.P. Dempsey, Plana's summation formula for
, Math. Comp. 55 (1990) 693-704. MR 91b:65003
- 6. M. Filonenko-Borodich, Theory of Elasticity, Mir Publishers, Moscow (1968).
- 7. W. Gautschi, On certain slowly convergent series occurring in plate contact problems , Math. Comp. 57, (1991) 325-338. MR 91j:40002
- 8. E.T. Whittaker and G.N. Watson, A course of modern analysis, C.U.P., Cambridge (1927).
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Additional Information
D. A. MacDonald
Affiliation:
Department of Mathematical Sciences, P.O. Box 147, The University, Liverpool L69 3BX, United Kingdom
Email:
sx10@liv.uk
DOI:
https://doi.org/10.1090/S0025-5718-97-00869-7
Keywords:
Slowly convergent series,
boundary value problems.
Received by editor(s):
July 10, 1996
Article copyright:
© Copyright 1997
American Mathematical Society