Degenerate Algorithms for degenerate Bernoulli and Euler numbers

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Authors: Taekyun Kim, Dae San Kim
Cited by: 0

Abstract

This paper introduces and investigates degenerate versions of the A-algorithm and B-algorithm by incorporating a parameter lambda into their respective recurrence relations. We derive explicit formulas for the final sequences of these algorithms in terms of the initial sequences and the degenerate Stirling numbers of the second kind. Furthermore, we establish functional relationships between the ordinary generating functions of the initial sequences and the exponential generating functions of the final sequences. Specifically, we demonstrate that these degenerate algorithms yield degenerate Bernoulli and Euler numbers under specific initial conditions.

Fields of Study & Subjects

Advanced Combinatorial Mathematics semigroups and automata theory Advanced Mathematical Identities

Publication details

Journal / source
arXiv (Cornell University)
Publication date
1 January 2026
Document type
Preprint