The Properties Of Special Polynomial And Promotion

The problem about Apostol-Bernoulli polynomial, Apostol-Euler polynomial and Apostol-Genocchi polynomial has been studied by many Chinese and foreign mathemati-cians. In this paper, by using the method of generatin function, we study the generalized Hermite-based Apostol-Euler polynomial containing parameters a, b, c and the properties with other polynomial series. Here we generalized the result of some special cases and thus get more related properties.The main results are as follows:The second chapter:Through the introduction of Hermite-KampedeFeriet poly-nomial, we defined the new generalized Hermite-based Apostol-Euler polynomials con-taining parameter a,b,c, on this basis, we study the nature of it, we can get a lot about generalized Hermite-based Apostol-Euler polynomial theorem and properties.The third chapter:Through the q-analogue method, we obtain another way of pro-motion of the Apostol-Euler polynomial, and this way promote the conclusion form more uniform, and in the actual calculation, there are also special convenient place.