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A Tauberian theorem for the logarithmic method of summation

Published online by Cambridge University Press:  24 October 2008

B. Kwee
B. Kwee
Affiliation:
University of Malaya, Kuala Lumpur
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Extract

The series is said to be summable (L) to sif

where sn = a0 + a1 + … + an, and it is said to be summable (l) to s if

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 2 , April 1967 , pp. 401 - 405
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Ishiguro, K.Tauberian theorems concerning the summability methods of Logarithmic type. Proc. Japan Acad. 39 (1963), 156–159.Google Scholar
(2)Ishiguro, K.A converse theorem on the summability methods. Proc. Japan Acad. 39 (1963), 38–41.Google Scholar
(3)Hardy, G. H.Divergent series (Oxford, 1949).Google Scholar
(4)Borwein, D.A logarithmic method of summability. J. Math. Soc. 33 (1958), 212–220.Google Scholar