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Multiple twisted \(q\)-Euler numbers and polynomials associated with \(p\)-adic \(q\)-integrals. (English) Zbl 1140.11311

Summary: By using \(p\)-adic \(q\)-integrals on \(\mathbb Z_{p}\), we define multiple twisted \(q\)-Euler numbers and polynomials. We also find Witt’s type formula for multiple twisted \(q\)-Euler numbers and discuss some characterizations of multiple twisted \(q\)-Euler Zeta functions. In particular, we construct multiple twisted Barnes’ type \(q\)-Euler polynomials and multiple twisted Barnes’ type \(q\)-Euler Zeta functions. Finally, we define multiple twisted Dirichlet’s type \(q\)-Euler numbers and polynomials, and give Witt’s type formula for them.

MSC:

11B68 Bernoulli and Euler numbers and polynomials
05A30 \(q\)-calculus and related topics
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