Analytic continuation of q-Euler numbers and polynomials

AbstractIn this work we study the q-Euler numbers and polynomials analytically continued to Eq(s). A new formula for Euler’s q-zeta function ζE,q(s) in terms of nested series of ζE,q(n) is derived. Finally we introduce the new concept of dynamics of the zeros of analytically continued q-Euler polynomials

Higher-order frobenius-Euler and poly-Bernoulli mixed type polynomials

In this paper, we consider higher-order Frobenius-Euler polynomi- als associated with poly-Bernoulli polynomials which are derived from polylogarithmic function. These polynomials are called higher-order Frobenius-Euler and poly-Bernoulli mixed type polynomials. The purpose of this paper is to give various identities of those polynomials arising from umbral calculus.Comment: 14 page