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Some identities on the \(q\)-Euler polynomials of higher order and \(q\)-Stirling numbers by the fermionic \(p\)-adic integral on \(\mathbb Z_p\). (English) Zbl 1192.05011

In this paper, the author discusses the higher-order \(q\)-Euler numbers and polynomials of Nörlund type by using the multivariate fermionic \(p\)-adic integral on \({\mathbb Z}_p\), then obtains a \(q\)-analog of identities for Stirling numbers.

MSC:

11B68 Bernoulli and Euler numbers and polynomials
11B73 Bell and Stirling numbers
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
05A19 Combinatorial identities, bijective combinatorics
05A15 Exact enumeration problems, generating functions
33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\)
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