On the higher-order \(w\)-\(q\)-Genocchi numbers. (English) Zbl 1187.05004

Summary: The main purpose of this paper is to study on higher-order \(w\)-\(q\)-Genocchi numbers and polynomials by using the \(p\)-adic \(q\)-deformed fermionic integral on \(\mathbb Z_p\). We derive some identities related to higher-order \(w\)-\(q\)-Genocchi numbers and polynomials. We also give interpolation functions of these numbers and polynomials.


11B65 Binomial coefficients; factorials; \(q\)-identities
05A15 Exact enumeration problems, generating functions
11B68 Bernoulli and Euler numbers and polynomials
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)