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Tauberian Theorems for Borel-Type Methods of Summability

Published online by Cambridge University Press:  20 November 2018

D. Borwein  and
E. Smet
D. Borwein
Affiliation:
University of Western Ontario
E. Smet
Affiliation:
University of Western Ontario
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Suppose throughout that s, an (n=0,1, 2,…) are arbitrary complex numbers, that α>0 and β is real and that N is a non-negative integer such that αN+β≧l. Let

where z=x+iy is a complex variable and the power zr is assumed to have its principal value.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 2 , 01 June 1974 , pp. 167 - 173
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Borwein, D., Relations between Borel-type methods of summability, Journal London Math. Soc, 35 (1960), 65-70.Google Scholar
2. Borwein, D., On methods of summability based on integral functions II, Proc. Camb. Phil. Soc, 56 (1960), 125-131.Google Scholar
3. Gaier, D., Zur Frage der Indexverschiebung beim Borel-Verfahren, Math. Zeit, 58 (1953), 453-455.Google Scholar
4. Hardy, G. H., Divergent series (Oxford, 1949).Google Scholar