  In the present paper, we introduce Eulerian polynomials with a and b
parameters and give the definition of them. By using the definition of
generating function for our polynomials, we derive some new identities in
Theory of Analytic Numbers. Also, we give relations between Eulerian
polynomials with a and b parameters, Bernstein polynomials, Poly-logarithm
function, Bernoulli numbers and Euler numbers. Moreover, we see that our
polynomials at a =-1 are related to Euler-Zeta function at negative inetegers.
Finally, we get Witt's formula for new generalization of Eulerian polynomials
which we express in this paper.
