On the highly accurate summation of certain series occurring in plate contact problems期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	D. A. MacDonald.

Affiliation:	Department of Mathematical Sciences, P.O. Box 147, The University, Liverpool L69 3BX, United Kingdom

Abstract:	The infinite series $R_p = sum _{k=1}^infty {(2 k - 1)}^{- p} , x^{2 k - 1}, 0 <1-xll 1 , p = 2 quad text {or} 3 , ,$ 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 , and will present new, rapidly convergent, series for and

Keywords:	Slowly convergent series boundary value problems.

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