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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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