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 ?
(because of asymptotic properties of Bessel function [mathematical expression not reproducible]), the absolute convergence of series (4.1) yields the absolute convergence of the series on the right of the last equality.
Keywords: Absolute convergence, Conditional convergence, Solow swan growth model, Pooled ordinary least square
At the same time, this assures absolute convergence of the vertical integral along s = - a + it.
(2010) report further evidence of absolute convergence in C[O.sub.2] emissions for 22 European countries over the period 1971-2006.
The absolute convergence type is defined by Galor as follows: "per capita incomes of countries converge to one another in the long run independently of their initial conditions".
Many authors deal with the subject of convergence and usually two types of convergence between different economies can be defined; these are absolute convergence and conditional convergence.
Therefore, the series of (15) is absolute convergence; that is, the sequence {[u.sub.k](x)} is convergent for x [member of] [a, b].
(Alternatively, for an analytic argument, the rearrangement is justified by absolute convergence.) Therefore
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.