The purpose of this paper is to introduce and study type 2 degenerate q
-Bernoulli polynomials and numbers by virtue of the bosonic p
-integrals. The obtained results are, among other things, several expressions for those polynomials, identities involving those numbers, identities regarding Carlitz’s q
-Bernoulli numbers, identities concerning degenerate q
-Bernoulli numbers, and the representations of the fully degenerate type 2 Bernoulli numbers in terms of moments of certain random variables, created from random variables with Laplace distributions. It is expected that, as was done in the case of type 2 degenerate Bernoulli polynomials and numbers, we will be able to find some identities of symmetry for those polynomials and numbers.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited