Fully degenerate Bernoulli numbers and polynomials - Kim Taekyun; Kim Dae San; Park Jin-Woo (Demonstratio Mathematica, 2022)
The aim of this article is to study the fully degenerate Bernoulli polynomials and numbers, which are a degenerate version of Bernoulli polynomials and numbers and arise naturally from the Volkenborn integral of the degenerate exponential functions on Zp{{\mathbb{Z}}}_{p}. We find some explicit expressions for the fully degenerate Bernoulli polynomials and numbers in terms of the degenerate Stirling numbers of the second kind, the degenerate rr-Stirling numbers of the second kind, and the degenerate Stirling polynomials. We also consider the degenerate poly-Bernoulli polynomials and derive explicit representations for them in terms of the same degenerate Stirling numbers and polynomials.