The Application Of Riordan Arrays In Annihilation Coefficients And General Riordan Group

Combinatorial identities which are an important aspect of combinatorial mathematics, has been widely applied to various subjects in the specific calculations. Looking for the methods about excavating and proving the combinatorial identity remains a meaningful research projects.In a variety of the methods of identifying and proofing the combinatorial identities,Riordan array is a very effective tool. This article will research the Riordan array from two aspects of the application and the promotion of the Riordan array.First,on the basis of the work of Louis W.Shapiro,H.W.Gould,Renzo Sprugnoli,L.C.Hsu and others,we will research the use of Riordan array in exploring the specific expression of Annihilation coefficient,and its application in the generalized Taylor expansions,trying to obtain a new series of combinatorial identities.Then this article will promote the theory of Riordan array,thus the generating function in the event no longer limited to the Taylor series,but extended to the Laurent series,at the same time,related theories have also been corresponding promoted.Finally this paper will discuss the convergence issues of the generalized Taylor expansion briefly.