Combinatorial Identities About The Generalized λ-Array Type Polynomials

In this paper, by using some Riordan array theory and generating functions, we derive some combinatorial identities, which are related to generalized A-array type poly-nomials, the generalized Hermite-based Apostol Bernoulli polynomials and the generalized Hermite-based Apostol Euler polynomials. In addition, some new identities involving the classical array type polynomials, the Stirling number of the second kind, the generalized Bernoulli polynomials and the generalized Euler polynomials is obtained. The main works can be summarized as follows:Chapter 2:In this chapter, we present a new class of the generalized λ-array type polynomials and some elementary properties of these polynomials by using generating function methods and take coefficient methods. In addition, we also investigate and in-troduce the generalized Hermite-based Apostol-Bernoulli polynomials, and derive some combinatorial relations between these polynomials and the generalized A-array type poly-nomials.Chapter 3:we use some exponential Riordan array theories to derive more combina-torial identities, which are related to generalized λ-array type polynomials, the generalized Hermite-based Apostol Bernoulli polynomials and the generalized Hermite-based Apos-tol Euler polynomials. Moreover, we also acquire some new more identities involving the classical array type polynomials, the Stirling number of the second kind, the generalized Bernoulli polynomials and the generalized Euler polynomials.