On the highly accurate summation of certain series occurring in plate contact problems
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- by D. A. MacDonald PDF
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Abstract:
The infinite series $R_p = \sum _{k=1}^\infty {(2 k - 1)}^{- p} x^{2 k - 1}$, $0 <1-x\ll 1$, $p = 2$ or $3$, and the related series \begin{equation*} \begin {split} C(x,b,2) &=\sum _{k=1}^\infty {(2k-1)}^{-2} \cosh (2k-1)x/\cosh (2k-1)b,\quad 0 <1-x/b \ll 1,\\ S(x,b,3)&=\sum _{k=1}^\infty {(2k-1)}^{-3} \sinh (2k-1)x/\cosh (2k-1)b, \end{split} \end{equation*} 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 $R_p$, and will present new, rapidly convergent, series for $C(x,b,2)$ and $S(x,b,3).$References
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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
- Received by editor(s): July 10, 1996
- © Copyright 1997 American Mathematical Society
- 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