Harmonic数是一种有趣的数列，在理论物理等方面有着重要的应用。有关它们的一个核心问题是相关恒等式的证明与计算。本项目旨在发掘各种常见的算子，如求导算子、有限差分算子、积分算子、留数算子等的应用规律，并将多种形式的算子进行统一，构造新的算子，系统研究(q-)Harmonic数恒等式的问题。包括（1）利用算子方法，通过对等式或函数表达式进行作用，系统研究Harmonic数恒等式的有关问题，并讨论在计算Riemann Zate级数等方面的应用；（2）利用算子方法及对称函数理论等，针对q-级数或含q的函数表达式来进行研究，探讨q-Harmonic数恒等式的问题，并找到它们在计算divisor函数及q-恒等式等方面的应用；（3）构造新的复合型算子，为研究(q-)Harmonic数恒等式提供新的工具。通过以上研究，将为(q-)Harmonic数的研究提供新的思路，从而发现更多有意义的恒等式。

Harmonic number is an interesting series, which has an important applications in theoretical physics etc.. Relating to their core issue is the calculation and proof of Harmonic number identities. This project aims to discover the application character of a variety of operators, such as the derivative operator, the finite difference operator, the integral operator, the residue operator and so on, and unify them, then construct new ones to study the (q-)Harmonic number identities systematically. These include: (1) applying the operational method to the equations and function expressions to study the Harmonic number identities, then discussing their applications on the calculation of the Riemann Zate series; (2) using the operational method and symmetric functions theory in q-series and the function expressions with q to study the q-Harmonic number identities, then discussing their applications on calculating the divisor function and q-identity； (3) constructing new and composite operators, and providing a new tool to study the (q-)Harmonic number identities. These studies will supply new ideas to (q-)Harmonic number, which can discover more meaningful identities.