Fully degenerate Bernoulli numbers and polynomials

Abstract

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.

Keywords

• fully degenerate bernoulli polynomials
• degenerate poly-bernoulli polynomials
• degenerate stirling numbers of the second kind
• degenerate r-stirling numbers of the second kind
• degenerate stirling polynomials
• 11b68
• 11b73
• 11b83