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Generating functions of the \((h,q)\) extension of twisted Euler polynomials and numbers. (English) Zbl 1174.11025

By using a \(p\)-adic \(q\)-deformed fermionic integral on \(\mathbb Z_p\), the authors construct new generating functions of the twisted \((h,q)\)-Euler numbers and polynomials attached to a Dirichlet character \(\chi\). By applying Mellin transformation and derivative operator to these functions, the author define twisted \((h,q)\)-extension of Euler numbers at negative integers. Furthermore, the authors construct the partially twisted \((h,q)\)-zeta function, and give some relations between the partially twisted \((h,q)\)-zeta function and twisted \((h,q)\)-extension of Euler numbers.

MSC:

11B68 Bernoulli and Euler numbers and polynomials
11S40 Zeta functions and \(L\)-functions
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
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