Application Of Generating Function And Riordan Array In Special Combination Sequence

In this thesis,we mainly study the application of generating function method and Riordan matrix method in special combinatorial sequences,and obtain the relationship between higher order Daehee polynomials,λ-Daehee polynomials and some special com-binatorial sequences.The main work of this thesis is as follows:First of all,using the methods of integration and derivation,combined with some operation skills,we can obtain the properties of λ-Daehee polynomials.Secondly,by using the method of generating function,some identities related to λ-Daehee numbers and polynomials are established.In the end,the higher order Daehee polynomials are studied by using the Riordan matrix method,and the new identities between the higher order Daehee polynomials and the classical combination sequences such as generalized Stirling number and Bernoulli number are obtained.