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Extended \(q\)-Euler numbers and polynomials associated with fermionic \(p\)-adic \(q\)-integral on \(\mathbb Z_{p}\). (English) Zbl 1132.33331
Summary: The purpose of this paper is to construct extended \(q\)-Euler numbers and polynomials related to fermionic \(p\)-adic \(q\)-integral on \(\mathbb Z_p\). By evaluating a multivariate \(p\)-adic \(q\)-integral on \(\mathbb Z_p\), we give new explicit formulas related to these numbers and polynomials.

MSC:
33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)
11B68 Bernoulli and Euler numbers and polynomials
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
33E50 Special functions in characteristic \(p\) (gamma functions, etc.)
82B10 Quantum equilibrium statistical mechanics (general)
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References:
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