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

Abstract

In [H. Ozden, Y. Simsek, I.N. Cangul, Generating functions of the (h, q)-extension of Euler polynomials and numbers, Acta Math. Hungarica, in press (doi:10.1007/510474-008-7139-1)], by using p-adic q-invariant integral on Z(P) in the fermionic sense, Ozden et al. constructed generating functions of the (h, q)-extension of Euler polynomials and numbers. They defined (h, q)-Euler zeta functions and (h, q)-Euler l-functions. They also raised the following problem: "Find a p-adic twisted interpolation function of the generalized twisted (h, q)-Eider numbers, E-n.chi.w((h))(q)". The aim of this paper is to give a partial answer to this problem. Therefore, we constructed twisted (h, q)-partial zeta function and twisted p-adic (h, q)-Euler l-functions which interpolate (h, q)-extension of Euler numbers, at negative integers by using this interpolation function and twisted (h, q)-partial zeta function, we proved distribution relations of the (h, q)-extension of generalized Euler polynomials. Consequently we find a partial answer to the above question. - To read graphics please open the file. -