Notes on Iterative Summation of Alternating Factorials

Vladimir Kanovei () and Vassily Lyubetsky ()
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Vladimir Kanovei: Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), 127051 Moscow, Russia
Vassily Lyubetsky: Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), 127051 Moscow, Russia

Mathematics, 2025, vol. 13, issue 12, 1-24

Abstract: The Eulerian iterative method of the summation of divergent series, invented in Institutiones Calculi Differentialis , is studied. We demonstrate that the method is equivalent to the Karamata–Lototsky–Jakimovski summability method, introduced in the 1950s. We prove a new theorem on the Euler iterative summability of the series of alternating factorials. Ensuing summability corollaries are discussed.

Keywords: divergent series; iterative summability; alternating factorials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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