Construction Of Combinatorial Identities Involving Harmonic Number

The combinatorial identity is one of the important contents of combinatorial mathematics research.The research methods include combination method,number theory method,probability method,complex analysis method and so on.In this paper,a combinatorial identity is constructed by means of hypergeometric function,and three combinational identities including higher order harmonic number are ob-tained by derivative operator.Difference formula is used in the another part of this paper,by backward difference operator,we construct a combinatorial identity.Then several summation formulas including higher order harmonic number are obtained by using derivative operator.Finally,the summation formulas including arbitrary order harmonic number are obtained and proved by mathematical induction.