A Note on Symmetric Properties of the Twisted -Bernoulli Polynomials and the Twisted Generalized -Bernoulli Polynomials

We define the twisted Open image in new window -Bernoulli polynomials and the twisted generalized Open image in new window -Bernoulli polynomials attached to Open image in new window of higher order and investigate some symmetric properties of them. Furthermore, using these symmetric properties of them, we can obtain some relationships between twisted Open image in new window -Bernoulli numbers and polynomials and between twisted generalized Open image in new window -Bernoulli numbers and polynomials.