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.

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.

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.
Application of Kronecker Summation Method in Computation of Robustly Stabilizing PI Controllers for Interval Plants, Proceedings of the 14th WSEAS International Conference on Systems, Corfu, Greece
The summation method just defined is not symmetric.
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.
In theory, the unitary method and the summation method should both reach the same conclusion: the value of the taxpayer's assets that are subject to property taxation.
In the summation method, each asset subject to taxation is appraised individually.
As an example of the foregoing, the summation method may be the leading method used in a property which is the ideal in every respect.
Alternatively, for Kronecker summation method, the matrix (6) is:
Application of Kronecker Summation Method in Computation of Robustly Stabilizing PI Controllers for Interval Plants, Manuscript submitted to The 14th WSEAS hnternational Conference on Systems, Corfu, Greece
Keywords Exponential sum, hyperbolic summation method, exponent pair.