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)lp,q(s,t|χ) for Dirchlet's character χ, with the property thatlp,q(−n,t|χ)=En,χn,q(pt)−[2]q[2]qpχn(p)[p]qnEn,χn,qp(t) for positive integers n   and t∈Cpt∈Cp with |t|p⩽1|t|p⩽1, and En,χn,q(x)En,χn,q(x) generalized Euler polynomials. Finally, we prove that lp,q(s,t|χ)lp,q(s,t|χ) is analytic in s and t   for s∈Cps∈Cp with |s|p