About Extensions of Generalized Apostol-Type Polynomials

Under a slight modification on the parameters associated to the generalized Apostol-type polynomials and the use of the generating method, we obtain some new results concerning extensions of generalized Apostol-type polynomials. We state some algebraic and differential properties for a new class of extensions of generalized Apostol-type polynomials, as well as, some others identities which connect this polynomial class with the Stirling numbers of second kind, the Jacobi polynomials, the generalized Bernoulli polynomials, the Genocchi polynomials and the Apostol-Euler polynomials, respectively.