Interpolation function of the (h,q)(h,q)-extension of twisted Euler numbers

In [H. Ozden, Y. Simsek, I.N. Cangul, Generating functions of the (h,q)(h,q)-extension of Euler polynomials and numbers, Acta Math. Hungarica, in press (doi:10.1007/510474-008-7139-1)], by using pp-adic qq-invariant integral on ZpZp in the fermionic sense, Ozden et al. constructed generating functions of the (h,q)(h,q)-extension of Euler polynomials and numbers. They defined (h,q)(h,q)-Euler zeta functions and (h,q)(h,q)-Euler ll-functions. They also raised the following problem: “Find a  pp-adic twisted interpolation function of the generalized twisted  (h,q)(h,q)-Euler numbers,  En,χ,w(h)(q)”. The aim of this paper is to give a partial answer to this problem. Therefore, we constructed twisted (h,q)(h,q)-partial zeta function and twisted pp-adic (h,q)(h,q)-Euler ll-functions: lE,p,ξ,q(h)(s,χ)=2∑m=1(m,p)=1∞χ(m)(−1)mξmqhmms, which interpolate (h,q)(h,q)-extension of Euler numbers, at negative integers: lE,p,ξ,q(h)(−n,χ)=En,ξ,χn(h)(q)−pnχn(p)En,ξp,χn(h)(qp). By using this interpolation function and twisted (h,q)(h,q)-partial zeta function, we proved distribution relations of the (h,q)(h,q)-extension of generalized Euler polynomials. Consequently we find a partial answer to the above question.