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Some explicit formulas for certain new classes of Bernoulli, Euler and Genocchi polynomials. (English) Zbl 1353.11031
Summary: In recent years, the subject of Apostol-Bernoulli polynomials, Apostol-Euler polynomials and Apostol-Genocchi polynomials have been studied extensively. Recently, the authors have introduced in [Honam Math. J. 34, No. 3, 311–326 (2012; Zbl 1327.11020); Int. J. Math. Math. Sci. 2012, Article ID 182785, 14 p. (2012; Zbl 1258.11047)] some new generalized classes of Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. In this paper, with the help of a result involving an explicit formula for the generalized potential polynomials obtained by M. Cenkci [Discrete Math. 309, No. 6, 1498–1510 (2009; Zbl 1213.11046)], we develop some explicit formulas related with these new classes of polynomials.

##### MSC:
 11B68 Bernoulli and Euler numbers and polynomials 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) 11B65 Binomial coefficients; factorials; $$q$$-identities