q-级数恒等式是q-级数理论的核心研究内容之一，与组合学、数论、theta级数理论、模形式理论等数学分支联系密切。本项目拟利用经典的解析方法和组合技巧改进已有的q-级数扩展公式、多重的Bailey引理、反演公式等工具，以系统研究Hecke-Rogers类型双重和级数恒等式及其截断性质，主要内容包括：.（1）构造全新的多重q-级数变换公式，给出若干经典q-级数公式的统一证明，及建立新的q-级数恒等式，着重讨论它们在Rogers-Ramanujan类型、Hecke-Rogers类型恒等式方面的应用，并推导出Hecke-Rogers双重和级数与mock theta函数之间的关系。.（2）探索q-级数恒等式的截断性质，将单重和级数的截断课题推广到与一些有意思的分拆函数相关的Hecke-Rogers类型双重和级数及多重和级数恒等式中。

The q-series identity is one of the core research contents of q-series theory, and it is closely related to some mathematical branches such as combinatorics, number theory, theta series theory, modular forms theory. The purpose of this project is to systematically study the Hecke-Rogers type identities and their truncated properties based on the modified q-series expansion formula，multiple Bailey lemma, inversion formula and other tools, which are obtained by classical analysis methods and combinatorial techniques. The main contents include:.(1) Establish new multiple q-transformation formulas, give unified proofs of some classical q-series identities, and establish new q-series identities, discuss their applications to Rogers-Ramanujan type and Hecke-Rogers type identities, as well as the relationship between Hecke-Rogers double series and mock theta functions..(2) Explore the truncated properties of q-series identities and extend this truncated subject of single sum series to Hecke-Rogers type double series identities and multiple q-series identities, which are associated with some interesting partition functions.