Representations by degenerate Bernoulli polynomials arising from Volkenborn integral

摘要

In this paper, we consider the problem of representing any polynomial in terms of the degenerate Bernoulli polynomials arising from Volkenborn integral and more generally of the higher‐order degenerate Bernoulli polynomials arising from iterated Volkenborn integral. We derive explicit formulas with the help of umbral calculus and illustrate our results with some examples.