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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



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
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 $|z| \leq 1$ and $p = 2$ or 3, as well as series of the type \[ \sum \limits _{k = 0}^\infty {{{(2k + 1)}^{ - p}}\cosh (2k + 1)x/\cosh (2k + 1)b} \] and \[ \sum \limits _{k = 0}^\infty {{{(2k + 1)}^{ - p}}\sinh (2k + 1)x/\cosh (2k + 1)b} \], 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.

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Keywords: Slowly convergent series, Laplace transformation, Stieltjes transform, orthogonal polynomials
Article copyright: © Copyright 1991 American Mathematical Society