On a p-adic interpolation function for the q-extension of the generalized Bernoulli polynomials and its derivative

Abstract. In [18], the new q-extension of Bernoulli polynomials and generalized Bernoulli numbers attached to χ were constructed by using p-adic invariant integral on Zp. In this paper we construct the new q-extension of generalized Bernoulli polynomials attached to χ due to author and derive the existence of a specific p-adic interpolation function which interpolate the q-extension of generalized Bernoulli polynomials at negative integer. Finally, we give the values of partial derivative for this function and investigate some properties which are related to this interpolation functions.