本项目计划应用或建立新的伴随根系统的WP-Bailey链，以及椭圆WP-Bailey链、高维矩阵反演、组合分析、行列式计算、交换和序等组合思想与方法为基本工具，研究伴随根系统的几类超几何级数与Mock Theta函数，建立一批创新性的重要结果，特别是给出C_n与椭圆WP-Bailey链的进一步应用，并且寻求新的方法和思想，从更高层次探索伴随根系统的几类超几何级数的突破；以及通过深入研究Mock Theta函数，回答Andrews千禧年提出的一个挑战问题，即阐明q级数的分类与模形式两者之间的重叠问题。本项目的目标是希望建立系统的方法，使我们的研究上一个台阶，取得前沿领域的创新性研究成果，促使伴随根系统的几类超几何级数与Mock Theta函数研究在国内的发展，形成一个有特色的研究团队。

By applying new WP-Bailey chain on root system, and elliptical WP-Bailey chain, high dimension matrix inversion, combinatorial analysis, determinant, exchange order of sum, etc. combinatorial thought and method as the basic tool, the project will research hypergeometric series of several types on root system and Mock theta functions to establish a number of important results, in particular, the further application is given on C_n and elliptic WP-Bailey chain, and seek new methods and ideas, explore hypergeometric series of several types on root system breakthrough from the higher level. By in-depth study of the Mock Theta function, answer a challenge problem proposed by Andrews in Millennium, that is the overlap between classes of q-series and modular forms.The goal of this project is to establish the systematic method, to obtain achievements frontiers, and construct the academic echelon to make our academic achievements to a new step, so that the hypergeometric series of several types on root system and Mock theta functions will have further development in China.