Research Of Harmonic Number Identities

Summation formulas involving generalized harmonic numbers are sysmatically explored in this thesis by utilizing the difference operator,derivative operator,integral operator,bi-jection method and hypergeometric method.These formulas not only include some known harmonic number identities as special cases,but also can produce a lot of new results.The concrete contents are displayed as follows:1.The first chapter introduces briefly the research methods and the development history of harmonic number identities.2.In the second chapter,we establish five classes of summation formulas involving generalized harmonic numbers in accordance with the difference operator.3.Based on Bailey-type 2-F1（1/2）-series,two classes of summation formulas involving generalized harmonic numbers are given in the third chapter by means of the derivative operator.4.Based on Dixon-type 3F₂（1）-series,we deduce two classes of summation formulas involving generalized harmonic numbers in the fourth chapter in terms of the derivative operator and bijection method of two-term sum.5.Based on Watson-type 3F₂（1）-series and Saalschütz-type 3F₂（1）-series,five classes of summation formulas involving generalized harmonic numbers are offered in the fifth chapter according to the derivative operator,integral operator and bijection method of two-term difference.6.The sixth chapter draws a conclusion of our work and makes some comments on the prospect of harmonic number identities.