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

Some identities of special numbers and polynomials arising from p$-adic integrals on Zp