Application Of Generating Function In Identities About Special Squences

Combinatorial identity is an important part of combinatorial mathematics,it is widely used in every branch of mathematics,and there are numerous ways to prove it.In this paper,we generalize the generating function of the Changhee-Genocchi polynomials,by means of the method of generating functions and Riordan arrays,we study the generalized Changhee-Genocchi polynomials,?-Changhee-Genocchi polynomials,?-Changhee polynomials,and establish some combinatorial identities between them and other special combinatorial sequences.The main results are as follows:1.We generalize the generating function of the Changhee-Genocchi polynomials,and study some properties of the generalized Changhee-Genocchi polynomials by means of the method of generating functions and Riordan arrays.At the same time,we establish some identities between the generalized Changhee-Genocchi polynomials and the n-th Twist Daehee polynomials,the higher-order Changhee numbers,the generalized Harnomic numbers,the Genocchi numbers,and other special combinatorial sequences.2.With the help of the generalized alternate falling factorial sums,the degenerate Bernoulli polynomials,and the degenerate Euler polynomials,we give some symmetric identities of ?-Changhee-Genocchi polynomials by using the generating function methods.In a similar way,we directly give some symmetric identities of ?-Changhee polynomials.