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

Abstract

In this paper we study a two-variable p-adic q– l-function l p , q ( s , t | χ ) for Dirchlet's character χ, with the property that l p , q ( − n , t | χ ) = E n , χ n , q ( p t ) − [ 2 ] q [ 2 ] q p χ n ( p ) [ p ] q n E n , χ n , q p ( t ) for positive integers n and t ∈ C p with | t | p ⩽ 1 , and E n , χ n , q ( x ) generalized Euler polynomials. Finally, we prove that l p , q ( s , t | χ ) is analytic in s and t for s ∈ C p with | s | p < p 1 − 1 p − 1 and t ∈ C p with | t | p ⩽ 1 .