Generalized w-Euler Numbers and Polynomials

Abstract EN

We generalize the Euler numbers and polynomials by the generalized w-Euler numbers En,w(a) and polynomials En,w(x:a).

For the complement theorem, En,w(x:a) have interesting different properties from the Euler polynomials and we observe an interesting phenomenon of “scattering” of the zeros of the the generalized Euler polynomials En,w(x:a) in complex plane.