???? −Bernoulli Matrices and Their Some Properties

Özet

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