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On certain slowly convergent series occurring in plate contact problems


Author: Walter Gautschi
Journal: Math. Comp. 57 (1991), 325-338
MSC: Primary 40A05; Secondary 44A10, 73K10, 73T05
DOI: https://doi.org/10.1090/S0025-5718-1991-1079018-7
MathSciNet review: 1079018
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Abstract: A simple computational procedure is developed for accurately summing series of the form $ \Sigma _{k = 0}^\infty {(2k + 1)^{ - p}}{z^{2k + 1}}$, where z is complex with $ \vert z\vert \leq 1$ and $ p = 2$ or 3, as well as series of the type

$\displaystyle \sum\limits_{k = 0}^\infty {{{(2k + 1)}^{ - p}}\cosh (2k + 1)x/\cosh (2k + 1)b} $

and

$\displaystyle \sum\limits_{k = 0}^\infty {{{(2k + 1)}^{ - p}}\sinh (2k + 1)x/\cosh (2k + 1)b} $

, where $ 0 \leq x \leq b$, $ p = 2$ or 3. The procedures are particularly useful in cases where the series converge slowly. Numerical experiments illustrate the effectiveness of the procedures.

References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1991-1079018-7
Keywords: Slowly convergent series, Laplace transformation, Stieltjes transform, orthogonal polynomials
Article copyright: © Copyright 1991 American Mathematical Society

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