On p-adic interpolating function for q-Euler numbers and its derivatives

In this paper we study a two-variable p-adic q–l-function lp,q (s, t |χ) for Dirchlet’s character χ, with the property that lp,q (−n, t |χ) = En,χn,q(pt) − [2]q [2]qp χn(p)[p]nq En,χn,qp (t) for positive integers n and t ∈ Cp with |t |p 1, and En,χn,q (x) generalized Euler polynomials. Finally, we prove that lp,q (s, t |χ) is analytic in s and t for s ∈ Cp with |s|p