This article presents a generalization of new classes degenerated Apostol–Bernoulli, Apostol–Euler, and Apostol–Genocchi Hermite polynomials level m. We establish some algebraic differential properties for generalizations Apostol–Bernoulli polynomials. These results are shown using generating function methods Apostol–Euler

In this paper, by using the Lipschitz summation formula, we obtain Fourier expansions and integral representations for the Genocchi polynomials. Some other new and interesting results are also shown.

In the vast literature in Analytic Number Theory, one can find systematic and extensive investigations not only of the classical Bernoulli, Euler and Genocchi polynomials and their corresponding numbers, but also of their many generalizations and basic (or q-) extensions. Our main object in this presentation is to introduce and investigate some of the principal generalizations and unifications ...

We introduce two biparametric families of Apostol-Frobenius-Euler polynomials level-$m$. give some algebraic properties, as well other identities which connect these polynomial class with the generalized $\lambda$-Stirling type numbers second kind, Apostol--Bernoulli polynomials, Apostol--Genocchi Apostol--Euler and Jacobi polynomials. Finally, we will show differential properties this new family

The main aim of this paper is to introduce and investigate the degenerate type 2-unified Apostol–Bernoulli, Euler Genocchi polynomials by using monomiality principle operational methods. We give explicit relations some identities for polynomials.

One finds several q-differential equations of a higher order for q-Euler polynomials and q-Genocchi polynomials. Additionally, we have few order, which are mixed with numbers Moreover, investigate some symmetric by applying properties

This paper presents a new generalization of the Genocchi numbers and theorem. As consequences, we obtain some important families integer-valued polynomials those are closely related to Bernoulli polynomials. Denoting by ${(B_n)}_{n \in \mathbb{N}}$ sequence ${(B_n(X))}_{n polynomials, especially that for any natural number $n$, reciprocal polynomial $\big(B_n(X) - B_n\big)$ is integer-valued.