The summation of a slowly convergent series
نویسندگان
چکیده
منابع مشابه
Method of summation of some slowly convergent series
A new method of summation of slowly convergent series is proposed. It may be successfully applied to the summation of generalized and basic hypergeometric series, as well as some classical orthogonal polynomial series expansions. In some special cases, our algorithm is equivalent to Wynn’s epsilon algorithm, Weniger transformation (Computer Physics Reports 10 (1989) 189371) or the technique rec...
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In a previous article the force between a dielectric cylinder and a conducting half-space for the cylinder approaching the half-space was obtained as the limit of a non-uniformly-convergent series. A special asymptotic analysis was performed to get a closed-form solution for this limit. The present article focuses on a delicate and crucial step in this analysis and gives a justification by a ma...
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The function in question is H(x) = ∑∞ k=1 sin(x/k)/k. In deference to the general theme of this conference, a summation procedure is first described using orthogonal polynomials and polynomial/rational Gauss quadrature. Its effectiveness is limited to relatively small (positive) values of x. Direct summation with acceleration is shown to be more powerful for very large values of x. Such values ...
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ژورنال
عنوان ژورنال: Edinburgh Mathematical Notes
سال: 1952
ISSN: 0950-1843,2051-2031
DOI: 10.1017/s0950184300002950