Moment Representations of Fully Degenerate Bernoulli and Degenerate Euler Polynomials

Abstract

Recently, the degenerate hyperbolic functions are studied in connection with the degenerate Bernoulli and degenerate Euler numbers which were introduced by Carlitz. The aim of this paper is to derive moment representations of the fully degenerate Bernoulli and degenerate Euler polynomials associated with the Laplace random variable with parameters \((a,b)=(0,1)\). In addition, we obtain the product expansions for the functions which are degenerate versions of \(\frac{\sinh t}{t}\) and \(\cosh t\). We also obtain some new identities involving the fully degenerate Bernoulli and degenerate Euler numbers by using series expansions for certain degenerate hyperbolic functions.

DOI 10.1134/S1061920824040071