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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