On the Symmetric Properties of Higher-Order Twisted <inline-formula><graphic file="1687-1847-2010-765259-i1.gif"/></inline-formula>-Euler Numbers and Polynomials

In 2009, Kim et al. gave some identities of symmetry for the twisted Euler polynomials of higher-order, recently. In this paper, we extend our result to the higher-order twisted -Euler numbers and polynomials. The purpose of this paper is to establish various identities concerning higher-order twisted -Euler numbers and polynomials by the properties of -adic invariant integral on . Especially, if , we derive the result of Kim et al. (2009).