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Zbl 1188.11006
Ryoo, C.S.; Kim, T.; Jang, Lee-Chae
Some relationships between the analogs of Euler numbers and polynomials. (English)
[J] J. Inequal. Appl. 2007, Article ID 86052, 22 p. (2007). ISSN 1029-242X/e

Summary: 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 $l$-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 $q$-Euler polynomials. Finally, we give a table for the solutions of the twisted $q$-Euler polynomials.

MSC 2000:: *11B68 Bernoulli numbers, etc.
33D15 Basic hypergeometric functions of one variable
11S40 Zeta functions and L-functions of local number fields

Keywords: twisted Euler polynomials; generating functions; twisted Euler numbers; twisted Euler zeta function; twisted Hurwitz zeta function; twisted Dirichlet $l$-Euler numbers; twisted Euler polynomials at non-positive integers; complex roots of twisted $q$-Euler polynomials

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