A new class of generalized Bernoulli polynomials and Euler polynomials

TL;DR

This paper introduces a new class of generalized Bernoulli and Euler polynomials based on q-integers, deriving q-analogues of classical formulas and identities involving q-Bernstein polynomials.

Contribution

It presents novel generalized Bernoulli and Euler polynomials using q-integers and derives new q-analogues of classical mathematical formulas.

Findings

Derived q-analogues of well-known formulas

Obtained a q-analogue of the Srivastava--Pintér addition theorem

Established new identities involving q-Bernstein 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--Pint\'er addition theorem is obtained. We give new identities involving q-Bernstein polynomials.