Divergent Series

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divergent series

[də′vər·jənt ′sir·ēz]
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 It might be outdated or ideologically biased.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.
References in periodicals archive ?
The Kronecker Summation Method for Robust Stabilization Applied to a Chemical Reactor.
Computation of stabilizing PI and PID controllers by using Kronecker summation method. Energy Conversion and Management, Vol.
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.
Summation Method. According to summation method, actual data is equal to predicted linear data summed up with error terms, as shown in the following equation:
Hence, final predictions from HIPM are obtained by summation method and multiplicative method as shown in the following two equations, respectively:
Finally we remark that a symmetric summation method in the time and frequency domain can be defined by
Unlike in the unitary method, few adjustments--or deductions--need to be made to the preliminary results of the summation method. This is because assets that are assessed separately or that are exempt from property taxation are never encompassed in the valuation analysis.
Alternatively, for Kronecker summation method, the matrix (6) is:
This paper uses the hyperbolic summation method and the exponential pair theory to obtain the asymptotic formula of [summation over n[less than or equal to]x] log [P.sub.ld](n).
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.