CONSTRUCTION FOR q-HYPERGEOMETRIC BERNOULLI POLYNOMIALS OF A COMPLEX VARIABLE WITH APPLICATIONS COMPUTER MODELING

Abstract

Two new extensions of the familiar Bernoulli polynomials are considered by using q-sine, q-cosine, q-hypergeometric and q-exponential functions. We call q-sine and q-cosine hypergeometric Bernoulli polynomials. Then, diverse formulas and properties for these polynomials, such as summation formulas, addition formulas, q-derivative properties, q-integral representations and some correlations are derived. Also, q-sine and q-cosine hypergeometric Bernoulli polynomials with two parameters are introduced and some relations and identities are investigated. Furthermore, some computational values are given by tables, and the beautiful zeros representations of the q-sine hypergeometric Bernoulli polynomials and q-cosine hypergeometric Bernoulli polynomials are showed by the figures