A New q -Analogue of Bernoulli Polynomials Associated with p -Adic q -Integrals

Abstract

We will study a new $q$-analogue of Bernoulli polynomials associated with $p$-adic $q$-integrals. Furthermore, we examine the Hurwitz-type $q$-zeta functions, replacing $p$-adic rational integers $x$ with a $q$-analogue ${\left[x\right]}_q$ for a $p$-adic number $q$ with , which interpolate $q$-analogue of Bernoulli polynomials.