Degenerate algorithms for degenerate Bernoulli and Euler numbers

Abstract

This paper introduces and investigates degenerate versions of the A-algorithm and B-algorithm by incorporating a parameter λ 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.