On the highly accurate summation of certain series occurring in plate contact problems

MacDonald, D.

doi:10.1090/S0025-5718-97-00869-7

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: The infinite series $R_p = \sum _{k=1}^\infty {(2 k - 1)}^{- p} \, x^{2 k - 1}, 0 <1-x\ll 1 ,\linebreak p = 2 \quad \text {or}\ 3 \, ,$ 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 $S(x,b,3).$

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