Absolute summability of infinite series on a scale of Abel type summability methods
Published online by Cambridge University Press: 24 October 2008
Extract
Suppose that λ > − 1 and that
It is easy to show that
With Borwein(1), we say that the sequence {sn} is summable Aλ to s, and write sn → s(Aλ), if the series
is convergent for all x in the open interval (0, 1)and tends to a finite limit s as x → 1 in (0, 1). The A0 method is the ordinary Abel method.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 2 , April 1968 , pp. 377 - 387
- Copyright
- Copyright © Cambridge Philosophical Society 1968
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