# absolutely convergent

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Related to absolutely convergent: Conditionally convergent

## absolutely convergent

Of, relating to, or characterized by absolute convergence.
References in periodicals archive ?
Since [absolute value of w(m)] = 1, the latter series, as the series for [[zeta].sub.n](s,[alpha], a), is absolutely convergent for [sigma] > 1/2.
When dealing with the absolutely convergent series [mathematical expression not reproducible], we take into account that
Due to the condition (2.1) the infinite product and the series in K(t, r) are absolutely convergent.
where the Dirichlet series G(s); = [[summation].sup.[infinity].sub.n = 1] g(n)/[n.sup.s][infinity] is absolutely convergent for Rs = [sigma] > 1/6.
(II) The integral [U.sub.[[rho]([absolute value of y'])+[alpha]]](x) is absolutely convergent. It represents a harmonic function on H and can be continuously extended to [bar.H] such that [U.sub.[[rho]([absolute value of y'])+[alpha]]](z') = u(z') for any z' [member of] [partial derivative]H;
be single-valued, regular and absolutely convergent for [sigma] > [[sigma].sub.a] and [sigma] > [[sigma].sub.b], respectively.
If a double series is absolutely convergent, then evidently the corresponding row-series and the columnseries are all absolutely convergent.
the integral being absolutely convergent for 1 < [sigma] < 2.
If [C.sub.0] > 1/2, the series is absolutely convergent.
For other types, we don't even know whether this integral is absolutely convergent on some right half-plane.
The first of them is a weighted limit theorem for absolutely convergent Dirichlet series.
is absolutely convergent in Re(s) > 1 and divergent in Re(s) < 1.
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