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

Abstract

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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Cited by in corpus (6)

• Generating functions for generalized Stirling type numbers, Array type polynomials, Eulerian type polynomials and their applications
• Analysis of the p-adic q-Volkenborn Integrals: an approach to Apostol-type special numbers and polynomials
• Some classes of generating functions for generalized Hermite- and Chebyshev-type polynomials: Analysis of Euler's formula
• Bell based Apostol type polynomials and its properties
• Differential equation and recurrence relations of the Sheffer-Appell polynomial sequence: A matrix approach
• Analysis of Bell based Euler polynomials and thier application