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Notes on Iterative Summation of Alternating Factorials

Author

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  • Vladimir Kanovei

    (Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), 127051 Moscow, Russia
    These authors contributed equally to this work.)

  • Vassily Lyubetsky

    (Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), 127051 Moscow, Russia
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Vladimir Kanovei & Vassily Lyubetsky, 2025. "Notes on Iterative Summation of Alternating Factorials," Mathematics, MDPI, vol. 13(12), pages 1-24, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:12:p:1942-:d:1676678
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    References listed on IDEAS

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    1. Trond Digernes & V. S. Varadarajan, 2010. "Notes on Euler’swork on divergent factorial series and their associated continued fractions," Indian Journal of Pure and Applied Mathematics, Springer, vol. 41(1), pages 39-66, February.
    2. Kanovei, Vladimir & Lyubetsky, Vassily, 2015. "Grossone approach to Hutton and Euler transforms," Applied Mathematics and Computation, Elsevier, vol. 255(C), pages 36-43.
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