Work

Notes on Iterative Summation of Alternating Factorials

Year: 2025

Type: article

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.

Source: Mathematics

DOI: 10.3390/math13121942

Authors: Vladimir Kanovei, Vassily Lyubetsky

Institutions: Russian Academy of Sciences, Institute for Information Transmission Problems

Language: English

Topic: Approximation Theory and Sequence Spaces

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Russian Science Foundation