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Summation by Euler’s transform of the series of Dirichlet, factorial series and the series of Newton. (English) Zbl 1463.40001

English translation of the author’s paper in Bulgarian [Ann. Univ. Sofia, Fac. Phys.-Math. 35, 1–156 (1939; Zbl 0026.10902)]. The present issue is published on the occasion of 120 years from the birth of Academician Obrechkoff (1896–1963), the 70th anniversary of the Institute of Mathematics and Informatics of Bulgarian Academy of Sciences (created October 1947) and 310 years from the birth of Leonard Euler (1717–1783).
For the Preface and Addendum to this article by P. Rusev, see [Zbl 1463.01039] and [Zbl 1463.40012].

MSC:

40-03 History of sequences, series, summability
40A05 Convergence and divergence of series and sequences
40G05 Cesàro, Euler, Nörlund and Hausdorff methods
01A75 Collected or selected works; reprintings or translations of classics
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