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Remarks on \(q\)-Bernoulli numbers associated with Daehee numbers. (English) Zbl 1188.05005
Summary: We study on Carlitz’s type \(q\)-Bernoulli numbers, \(q\)-Frobenius-Euler numbers and Daehee numbers and polynomials. We also give \(p\)-adic integral representation of the twisted Daehee polynomials. By using this representation, we find Raabe-type multiplication formula for the twisted Daehee polynomials.

MSC:
11B68 Bernoulli and Euler numbers and polynomials
05A10 Factorials, binomial coefficients, combinatorial functions
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
11B65 Binomial coefficients; factorials; \(q\)-identities
33D99 Basic hypergeometric functions
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