  In recent years, studying degenerate versions of various special polynomials
and numbers have attracted many mathematicians. Here we introduce degenerate
type 2 Bernoulli polynomials, fully degenerate type 2 Bernoulli polynomials and
degenerate type 2 Euler polynomials, and their corresponding numbers, as
degenerate and type 2 versions of Bernoulli and Euler numbers. Regarding to
those polynomials and numbers, we derive some identities, distribution
relations, Witt type formulas and analogues for the Bernoulli's interpretation
of powers of the first $m$ positive integers in terms of Bernoulli polynomials.
The present study was done by using the bosonic and fermionic $p$-adic
integrals on $\mathbb{Z}_p$.

Number Theory