Strong summability of infinite series on a scale of Abel type summability methods
Published online by Cambridge University Press: 24 October 2008
Extract
Introduction. In a recent paper, Borwein(1) constructed a new method of summability which would read: Let
and let {sn} be any sequence of numbers. If, for λ > − 1,
is convergent for all x in the open interval (0,1) and tends to a finite limit s as x → 1 in (0,1), we say that the sequence {sn} is Aλ convergent to s and write sn → s(Aλ). The A0 method is the ordinary Abel method.
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- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 1 , January 1967 , pp. 119 - 127
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- Copyright © Cambridge Philosophical Society 1967
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