Some Relationships between the Analogs of Euler Numbers and Polynomials

We construct new twisted Euler polynomials and numbers. We also study the generating functions of the twisted Euler numbers and polynomials associated with their interpolation functions. Next we construct twisted Euler zeta function, twisted Hurwitz zeta function, twisted Dirichlet[inline-graphic not available: see fulltext]-Euler numbers and twisted Euler polynomials at non-positive integers, respectively. Furthermore, we find distribution relations of generalized twisted Euler numbers and polynomials. By numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the twisted[inline-graphic not available: see fulltext]-Euler polynomials. Finally, we give a table for the solutions of the twisted[inline-graphic not available: see fulltext]-Euler polynomials.