Some Recurrence Formulas for the q-Bernoulli and q-Euler Polynomials

Abstract

The recurrence relations have a very important place for the special
polynomials such as $q$-Appell polynomials. In this paper, we give some
recurrence formulas that allow us a better understanding of $q$-Appell
polynomials. We investigate the $q$-Bernoulli polynomials and $q$-Euler
polynomials, which are $q$-Appell polynomials, and we obtain their
recurrence formulas by using the methods of the $q$-umbral calculus and the
quantum calculus. Our methods include some operators which are quite handy
for obtaining relations for the $q$-Appell polynomials. Especially, some
applications of $q$-derivative operator are used in this work.