𝑞 −Bernoulli Matrices and Their Some Properties

Abstract

In this study, we define 𝑞 −Bernoulli matrix B( ) q and 𝑞 −Bernoulli polynomial matrix B( , ) x q by using 𝑞 −Bernoulli numbers, and polynomials respectively. We obtain some properties of B( ) q and B( , ) x q . We obtain factorizations 𝑞 −Bernoulli polynomial matrix and shifted 𝑞 −Bernoulli matrix using special matrices.