A simple approach to the summation of certain slowly convergent series. (English) Zbl 0808.40001
Summary: Summation of series of the form \(\sum^ \infty_{k = 1} k^{\nu-1} r(k)\) is considered, where \(0 \leq \nu \leq 1\) and \(r\) is a rational function. By an application of the Euler-Maclaurin summation formula, the problem is reduced to the evaluation of Gauss’ hypergeometric function. Examples are given.
MSC:
| 40A25 | Approximation to limiting values (summation of series, etc.) |
| 65D30 | Numerical integration |
| 65B15 | Euler-Maclaurin formula in numerical analysis |
Keywords:
slowly convergent series; summation of series; Euler-Maclaurin summation formula; Gauss’ hypergeometric functionReferences:
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