absolute convergence


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absolute convergence

[′ab·sə‚lüt kən′vərj·əns]
(mathematics)
That property of an infinite series (or infinite product) of real or complex numbers if the series (product) of absolute values converges; absolute convergence implies convergence.
References in periodicals archive ?
At the same time, this assures absolute convergence of the vertical integral along s = - a + it.
The paper is structured as follows: an introductory section that defines the subject matter and presents the basis of the distinction between the extremely important concepts of environmental fiscal pressure and environmental fiscal effort; a second section detailing the methodology employed, both in the absolute convergence analysis and the spatial dependency comparison; and a third section that presents the results of the study and finally the conclusions.
backward regional economic growth will be compared with the developed region faster; phase reverse if b is greater than 0, corresponding [beta] will be less than 0, then there is no absolute convergence.
If this set of structural exogenous variables is excluded, absolute convergence is presumed.
Absolute convergence exists if 0 < [gamma] < 1 ; < [gamma] > 1 would suggest divergence.
Using the monotonicity respectively the absolute convergence in our setting of the rvs Rn we obtain under weak conditions the convergence to a limiting rv R and also continuity in mean.
As expected, no evidence of absolute convergence could be observed obviously due to presence of vast differences across the provinces in terms of the growth determinants.
Hence, letting p [right arrow] [infinity] in (12)-(14) and considering the absolute convergence of the obtained double series, we get the following theorem.
and [zeta](s), which is justified by absolute convergence of both series for [sigma] > 1, gives Eq.
In Section 2, we give some tests for absolute convergence of a double series including analogues of Cauchy's Condensation Test, Abel's kth Term Test, Limit Comparison Test, Ratio Test, Ratio Comparison Test, and Raabe's Test.
The sufficient conditions for the absolute convergence of the integral have been established by Buschman and Srivastava [1, p.
In such a setting, the absolute convergence of all countries is impossible.