Abstract
We generalize the Euler numbers and polynomials by the generalized -Euler numbers and polynomials . For the complement theorem, 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 in complex plane.
Highlights
The Euler numbers and polynomials possess many interesting properties and arising in many areas of mathematics and physics
We investigate some properties which are related to the generalized w-Euler numbers En,w a and polynomials En,w x : a
We find generating functions of the generalized w-Euler numbers En,w a and polynomials En,w x : a
Summary
The Euler numbers and polynomials possess many interesting properties and arising in many areas of mathematics and physics. In 14 , we introduced that Euler equation En x 0 has symmetrical roots for x 1/2 see 14 It is the aim of this paper to observe an interesting phenomenon of “scattering” of the zeros of the the generalized wEuler polynomials En,w x : a in complex plane. Our aim in this paper is to define the generalized w-Euler numbers En,w a and polynomials En,w x : a. We investigate some properties which are related to the generalized w-Euler numbers En,w a and polynomials En,w x : a. We derive the existence of a specific interpolation function which interpolate the generalized w-Euler numbers En,w a and polynomials En,w x : a
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