Unification of the three families of generalized Apostol type polynomials on the Umbral algebra

Details Unification of the three families of generalized Apostol type polynomials on the Umbral algebra Unification of the three families of generalized Apostol type polynomials on the Umbral algebra

2011-10-07

arxiv.org/abs/1110.2047v1

Mathematics

Classical Analysis and ODEs

Scientific paper

The aim of this paper is to investigate and introduce some new identities related to the unification and generalization of the three families of generalized Apostol type polynomials, which are Apostol-Bernoulli, Apostol-Euler, and Apostol-Genocchi polynomials, on the modern theory of the Umbral calculus and algebra. We also introduce some operators. Recently, Ozden constructed generating function of the unification of the Apostol type polynomials (see Ozden [H. Ozden, AIP Conf. Proc. 1281, (2010), 1125-1227.]). By using this generating function, we derive many properties of these polynomials. We give relations between these polynomials and Stirling numbers.

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