? −Bernoulli Matrices and Their Some Properties

? −Bernoulli Matrices and Their Some Properties

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.

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