A~connection between the summability methods of Cesaro and Lambert
Matematičeskie zametki, Tome 5 (1969) no. 5, pp. 521-526.

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We show that if a series is $(C,k)$ summable for some $k>-1$, then it is $(L,\alpha)$ summable to the same sum for any $\alpha2$.
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     author = {I. I. Zhogin},
     title = {A~connection between the summability methods of {Cesaro} and {Lambert}},
     journal = {Matemati\v{c}eskie zametki},
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I. I. Zhogin. A~connection between the summability methods of Cesaro and Lambert. Matematičeskie zametki, Tome 5 (1969) no. 5, pp. 521-526. http://geodesic.mathdoc.fr/item/MZM_1969_5_5_a2/