  The present paper deals with unification of the multiple twisted Euler and
Genocchi numbers and polynomials associated with p-adic q-integral on Zp at q =
1. Some earlier results of Ozden's papers in terms of unification of the
multiple twisted Euler and Genocchi numbers and polynomials associated with
p-adic q-integral on Zp at q = 1 can be deduced. We apply the method of
generating function and p-adic q-integral representation on Zp, which are
exploited to derive further classes of Euler polynomials and Genocchi
polynomials. To be more precise we summarize our results as follows, we obtain
some relations between H.Ozden's generating function and fermionic p-adic
q-integral on Zp at q = 1. Furthermore we derive Witt's type formula for the
unification of twisted Euler and Genocchi polynomials. Also we derive
distribution formula (Multiplication Theorem) for multiple twisted Euler and
Genocchi numbers and polynomials associated with p-adic q-integral on Zp at q =
1 which yields a deeper insight into the effectiveness of this type of
generalizations. Furthermore we define unification of multiple twisted zeta
function and we obtain an interpolation formula between unification of multiple
twisted zeta function and unification of the multiple twisted Euler and
Genocchi numbers at negative integer. Our new generating function possess a
number of interesting properties which we state in this paper.

Number Theory