Divergent Series

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divergent series

[də′vər·jənt ′sir·ēz]
(mathematics)
An infinite series whose sequence of partial sums does not converge.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Divergent Series

 

a series in which the sequence of partial sums does not have a finite limit. If the general term of the series does not tend to zero, the series diverges, for example, 1 - 1 + 1 - 1 + … + (– 1)n-1. The harmonic series 1 + 1/2 + … + 1/2 + … is an example of a divergent series whose general term tends to zero. There exist numerous classes of divergent series that converge in some generalized sense, since to each such divergent series some “generalized sum” may be assigned that possesses the most important properties of the sum of a convergent series.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
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The Kronecker Summation Method for Robust Stabilization Applied to a Chemical Reactor.
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The results for the proposed method were compared with those by our previous method and a simple summation method in which the multiple images were just summed without any registration.
The simple summation method produced a blurred tumor.
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Finally we remark that a symmetric summation method in the time and frequency domain can be defined by
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Alternatively, for Kronecker summation method, the matrix (6) is:
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We compare the frequency responses of, the Green's functions, and the mean errors from the three modal summation methods using MoM solution as the reference.
It may be categorized as Current summation methods, Power summation methods and admittance summation methods.