A New Family of Zeta Type Functions Involving the Hurwitz Zeta Function and the Alternating Hurwitz Zeta Function

In this paper, we further study the generating function involving a variety of special numbers and ploynomials constructed by second author. Applying Mellin transformation to function, define new class zeta type functions, which is related interpolation functions Apostol–Bernoulli polynomials, Bernoulli Euler polynomials. This Hurwitz alternating Lerch function. Furthermore, using these derive some identities combinatorial sums polynomials