Various Structures of the Roots and Explicit Properties of <i>q</i>-cosine Bernoulli Polynomials and <i>q</i>-sine Bernoulli Polynomials

Abstract

In this paper, we define cosine Bernoulli polynomials and sine Bernoulli polynomials related to the q-number. Furthermore, we intend to find the properties of these polynomials and check the structure of the roots. Through numerical experimentation, we look for various assumptions about the polynomials above.

Keywords

• <i>q</i>-cosine bernoulli polynomials
• <i>q</i>-sine bernoulli polynomials
• <i>q</i>-numbers
• <i>q</i>-trigonometric function