| Summary: | The purpose of this paper is to introduce and study type 2 degenerate <i>q</i>-Bernoulli polynomials and numbers by virtue of the bosonic <i>p</i>-adic <i>q</i>-integrals. The obtained results are, among other things, several expressions for those polynomials, identities involving those numbers, identities regarding Carlitz’s <i>q</i>-Bernoulli numbers, identities concerning degenerate <i>q</i>-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.
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