Advances in Difference Equations (Jan 2010)
A Note on Symmetric Properties of the Twisted <inline-formula><graphic file="1687-1847-2010-801580-i1.gif"/></inline-formula>-Bernoulli Polynomials and the Twisted Generalized <inline-formula><graphic file="1687-1847-2010-801580-i2.gif"/></inline-formula>-Bernoulli Polynomials
Abstract
We define the twisted -Bernoulli polynomials and the twisted generalized -Bernoulli polynomials attached to of higher order and investigate some symmetric properties of them. Furthermore, using these symmetric properties of them, we can obtain some relationships between twisted -Bernoulli numbers and polynomials and between twisted generalized -Bernoulli numbers and polynomials.