Research On A Class Of Shifted-Harmonic Number Identities

In this paper,the author focuses on combinatorial identities containing sums of higher-order Shifted-Harmonic numbers,based on the proof of combinatorial identities already given by other scholars.It is mainly to build a meaningful set of combinatorial identities about Euler summations using partial fractional mathematical methods and mathematical ideas with the help of recursive iterations.Specific content includes:(1)The sum formula of the reciprocal product containing higher-order Shifted-Harmonic numbers and binomial coefficients was studied mainly by partial fractional unfolding,such as the exploration of the series(?),and explored the form of a series to obtain meaningful harmonic identities.(2)Using the partial fractional method,the Hamonic numbers in the molecule are deformed,and the corresponding higher-order Alternating Shifted-Harmonic number identity(?)is further studied,and more concise and beautiful identities about Alternating Shifted-Harmonic numbers are found.(3)Using the technique of finite summation of series,the partial fractional method is used to further study the finite summation series containing higher-order Alternating Shifted-Harmonic numbers.The series(?)was studied and generalized,and a lot of meaningful identities were obtained.