On the Relation between the Logarithmic and Borel-Type Summability Methods
Canadian mathematical bulletin, Tome 24 (1981) no. 2, pp. 153-159

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Suppose throughout that {sn} is a sequence of real numbers, λ > - 1, a > 0, and β is real. Let N be any non-negative integer such that αN + β > l.We are concerned primarily with the logarithmic summability method L and the Borel-type method (B, α, β). Some known results involve the Abel-type summability method Aγ.
Borwein, D.; Watson, B. On the Relation between the Logarithmic and Borel-Type Summability Methods. Canadian mathematical bulletin, Tome 24 (1981) no. 2, pp. 153-159. doi: 10.4153/CMB-1981-025-0
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[1] 1. Borwein, D., On methods of summability based on power series, Proc. Royal Soc. Edinburgh. 64 (1957), 342-349. Google Scholar

[2] 2. Borwein, D., A logarithmic method of summability, Journal London Math. Soc.. 33 (1958), 212-220. Google Scholar

[3] 3. Borwein, D. and Watson, B., Tauberian theorems on a scale of Abel-type summability methods, Journal fur die Reine und Angewandte Mathematik. 298 (1978), 1-7. Google Scholar

[4] 4. Borwein, D., Tauberian theorems between the logarithmic and Abel-type summability methods, submitted for publication. Google Scholar

[5] 5. Hardy, G. H., Divergent Series, Oxford (1949). Google Scholar

[6] 6. Shawyer, B. L. R. and Yang, G. S., On the relation between the Abel-type and Borel-type methods of summability, Proc. Amer. Math. Soc.. 26 (1970), 323-328. Google Scholar

[7] 7. Shawyer, B. L. R. and Yang, G. S., Tauberian relations between the Abel-type and the Borel-type methods of summability, Manuscripta Math.. 5 (1971), 341-357. Google Scholar

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