absolute convergence

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Related to absolutely convergent: Conditionally convergent

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 ?
It is easily seen the Dirichlet series is absolutely convergent for Rs = [sigma] > 1/6.
ii) Each row-series as well as each column-series is absolutely convergent.
k,l] is absolutely convergent if and only if the following conditions hold: (i) There are ([k.
is absolutely convergent for [sigma] < O, since the term in square brackets vanishes for 0 [less than or equal to] x < 1 by (11).
It is easily seen that H(s) can be written as Dirichlet series which is absolutely convergent for [Real part]s > 1/6.
By the properties of Dirichlet series, the later one is absolutely convergent for Res > 1/5.
It is easily seen that G(s) can be written as a Dirichlet series, which is absolutely convergent for Rs > 1/5.
where G(s) can be written as an infinite Dirichlet series, which is absolutely convergent for [sigma] > 1/2.
It is easy to prove that the series is absolutely convergent Res > [epsilon] > 0.
For any real number s > 1, the series (2) is absolutely convergent, and
6 of [2]) we know that the infinite series can be expressed as an absolutely convergent infinite product.
m](n) [much less than] n, so it is clear that f(s) is an absolutely convergent series for Re(s) > 2, by the Euler product formula [2] and the definition of [[delta].