Some new identities for the Apostol–Bernoulli polynomials and the Apostol–Genocchi polynomials

Identities related to the Stirling numbers and modified Apostol-type numbers on Umbral Calculus

“…The authors thank the anonymous referee to show us a related article [12], which appeared independently during the long process of this article, as well as the additional references [3,7,8,11,25,26].…”

General convolution identities for Apostol-Bernoulli, Euler and Genocchi polynomials

“…If we take k = 2 in Corollary 4.3, by applying the methods described in [14] to yield (2.18), we obtain another convolution identity for the classical Genocchi polynomials due to Agoh [1,20], namely…”

“…If we take k = 2 in (4.5), in view of G 0 = 0 and G 1 = 1 (see, e.g., [27]), we get the convolution identity for the classical Genocchi polynomials due to Agoh [1,20], namely…”

Some formulas for the generalized Apostol-type polynomials and numbers

“…Since the publication of the above works by Luo and Srivastava, numerous properties for the generalized Apostol-Bernoulli polynomials, Euler and Genocchi polynomials have been studied. We refer to [5,7,8,15,17,20,21,25] for some related results on these Apostol-type polynomials and numbers. In [24,26], Ozden et al, constructed the following generating function:…”