Some identities on the generalized \(q\)-Bernoulli, \(q\)-Euler, and \(q\)-Genocchi polynomials
Summary: \textit{N. I. Mahmudov} [Discrete Dyn. Nat. Soc. 2012, Article ID 169348, 8 p. (2012; Zbl 1253.11027) and ``On a class of \(q\)-Bernoulli and \(q\)-Euler polynomials,'' Adv. Difference Equ. 2013, Article 108 (2013), \url{http://dx.doi.org/10.1186/1687-1847-2013-108}] introduced and investigated some \(q\)-extensions of the \(q\)-Bernoulli polynomials \(\mathcal B^{(\alpha)}_{n,q}(x,y)\) of order \(\alpha\), the \(q\)-Euler polynomials \(\mathcal E^{(\alpha)}_{n,q}(x,y)\) of order \(\alpha\), and the \(q\)-Genocchi polynomials \(\mathcal G^{(\alpha)}_{n,q}(x,y)\) of order \(\alpha\). In this paper, we give some identities for \(\mathcal B^{(\alpha)}_{n,q}(x,y)\), \(\mathcal G^{(\alpha)}_{n,q}(x,y)\), and \(\mathcal E^{(\alpha)}_{n,q}(x,y)\) and the recurrence relations between these polynomials. This is an analogous result to the \(q\)-extension of the Srivastava-Pintér addition theorem in Mahmudov (2013, loc. cit.).
scientific article; zbMATH DE number 6306625
scientific article