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On Absolute Summability for any Positive Order

Published online by Cambridge University Press:  20 January 2009

C. E. Winn
C. E. Winn
Affiliation:
(Egyptian University).
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Absolute summability according to Cesàro's method has been defined by Fekete for positive integral orders, as follows:—

Denoting the rth partial sum of a series Σun by and its rth mean, namely2, by we can regard as the sum of the series

.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 3 , Issue 3 , February 1933 , pp. 173 - 178
Copyright
Copyright © Edinburgh Mathematical Society 1933

References

page 173 note 1 Math, ès Term. Ert. (1911), pp. 719–726.Google Scholar

page 173 note 2

page 175 note 1 If i or j is zero, we omit the corresponding sum.

page 176 note 1 an–1, n vanishes, if we take . This follows, if we suppose true for n = 0.

page 177 note 1 It should be observed that Σ1 and Σ2 do not occur when k = 0.