A new class of generalized Bernoulli polynomials and Euler polynomials

Abstract

The main purpose of this paper is to introduce and investigate a new class of generalized Bernoulli polynomials and Euler polynomials based on the q-integers. The q-analogues of well-known formulas are derived. The q-analogue of the Srivastava--Pintér addition theorem is obtained. We give new identities involving q-Bernstein polynomials.

References in corpus (4)

• $q$-Bernoulli Numbers and Polynomials Associated with Multiple $q$-Zeta Functions and Basic $L$-series
• A note on q-Euler numbers and polynomials
• The Modified q-Euler numbers and polynomials
• On the q-Extensions of the Bernoulli and Euler Numbers, Related Identities and Lerch Zeta Function