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Absolute summability of infinite series on a scale of Abel type summability methods

Published online by Cambridge University Press:  24 October 2008

Babban Prasad Mishra
Babban Prasad Mishra
Affiliation:
Department of Mathematics, The University, Gorakhpur, India
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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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References

REFERENCES

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