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On Tauberian theorems for Abel-Cesàro summability
Published online by Cambridge University Press: 18 May 2009
Extract
For a series Σan with partial sums An=a0 + a1 + … + an(n ≥ 0), supposed to be real in this note, we define, in a generally accepted notation ([2], pp. 7, 9, 94–98), the following transforms:
(C, α) sequence-transform,
(H, k)sequence-transform (k = 0, 1, 2, …):
(A: C, α)fnunction-transform,
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- Copyright © Glasgow Mathematical Journal Trust 1958
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