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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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On certain slowly convergent series occurring in plate contact problems
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by Walter Gautschi PDF
Math. Comp. 57 (1991), 325-338 Request permission

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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Additional Information
  • © Copyright 1991 American Mathematical Society
  • 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