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Mathematics
Volume 13
Issue 12
10.3390/math13121942
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Article

Notes on Iterative Summation of Alternating Factorials

by
Vladimir Kanovei
* and
Vassily Lyubetsky
*
Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), 127051 Moscow, Russia
*
Authors to whom correspondence should be addressed.
Mathematics 2025, 13(12), 1942; https://doi.org/10.3390/math13121942
Submission received: 20 April 2025 / Revised: 27 May 2025 / Accepted: 3 June 2025 / Published: 11 June 2025
Versions Notes

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 divergent series; iterative summability; alternating factorials

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MDPI and ACS Style

Kanovei, V.; Lyubetsky, V. Notes on Iterative Summation of Alternating Factorials. Mathematics 2025, 13, 1942. https://doi.org/10.3390/math13121942

AMA Style

Kanovei V, Lyubetsky V. Notes on Iterative Summation of Alternating Factorials. Mathematics. 2025; 13(12):1942. https://doi.org/10.3390/math13121942

Chicago/Turabian Style

Kanovei, Vladimir, and Vassily Lyubetsky. 2025. "Notes on Iterative Summation of Alternating Factorials" Mathematics 13, no. 12: 1942. https://doi.org/10.3390/math13121942

APA Style

Kanovei, V., & Lyubetsky, V. (2025). Notes on Iterative Summation of Alternating Factorials. Mathematics, 13(12), 1942. https://doi.org/10.3390/math13121942

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