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

AbstractIn [T. Kim, S.H. Rim, Generalized Carlitz’s q-Bernoulli numbers in the p-adic number field, Adv. Stud. Contemp. Math. 2 (2000) 9–19], 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 interpolates the q-extension of generalized Bernoulli polynomials at negative integers. Finally, we give the values of partial derivative for this function and investigate some properties which are related to this interpolation function