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Errata: “On the introduction of convergence factors into summable series and summable integrals” [Trans. Amer. Math. Soc. 8 (1907), no. 2, 299–330; 1500786] [PDF]
Transactions of the American Mathematical Society, 1907 openaire +1 more source
On |R, log n, 1|-summability factors of power series on ist circle of convergence.
Srivastava, V.P. +2 more
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Convergence and summability factors in a sequence (II)
Mathematika, 1983L S Bosanquet
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On the factorable spaces of absolutelyp-summable, null, convergent, and bounded sequences
Mathematica Slovaca, 2021AbstractLetFdenote the factorable matrix andX∈ {ℓp,c0,c,ℓ∞}. In this study, we introduce the domainsX(F) of the factorable matrix in the spacesX. Also, we give the bases and determine the alpha-, beta- and gamma-duals of the spacesX(F). We obtain the necessary and sufficient conditions on an infinite matrix belonging to the classes (ℓp(F),ℓ∞), (ℓp(F),f)
Başar, Feyzi, Roopaei, Hadi
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An Estimate of the Rate of Convergence for the Absolute Summability of Factors of Infinite Series
Power System Technology, 2023Here in, we provide evidence of three theorems about a special case of the absolute summing-up-factors of infinite series using much less stringent conditions. Some particular results on various absolute summability approaches also been produced. The papers [7], [21], and [22] serve inspirations for our work.
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On convergence and summability factors in a sequence
Mathematika, 1954It is familiar that if Ean is convergent and en is positive and decreasing then Eansn is convergent (Abel's test). More generally du Bois-Reymond and Dedekind (sufficiency) and Hadamard (necessity) showed that a necessary and sufficient condition for Eanen to converge whenever Ean converges is that en be of bounded variation.
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Borel Summability and Converging Factors for Some Everywhere Divergent Series
SIAM Journal on Mathematical Analysis, 1986The author studies the formal power series (everywhere divergent) \(F(z)=\sum^{\infty}_{r=1}a_ rz^ r\), where \(a_ r=r^ pw(r)(r!)^ m,\) \(p\geq 0\), \(m\geq 1\) are integers and w(r) is such that for some \(\sigma >0\), \(w(r)\sim \sum^{\infty}_{i=0}w_ ir^{-i- \sigma},\) as \(r\to \infty\).
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