Remarks on \(q\)-Bernoulli numbers associated with Daehee numbers. (English) Zbl 1188.05005

Özden, Hacer; Cangül, İsmail Naci; Simsek, Yilmaz

Adv. Stud. Contemp. Math., Kyungshang 18, No. 1, 41-48 (2009).

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

Keywords:

\(p\)-adic integral; twisted Daehee numbers; twisted Daehee polynomials; Bernoulli numbers; Bernoulli polynomials; Euler numbers