标题： 基本超几何恒等式来自三重关系 显示英文标题

标题： Basic hypergeometric identities derived from three-term relations

摘要： 2015年，Ebisu提出了一种新的寻找超几何恒等式的方法，该方法基于${}_{2} F_{1}$超几何级数的三项关系。 通过这种方法，他推导出了几乎所有已知的超几何恒等式，以及许多新的恒等式。 在本文中，我们通过将Ebisu方法的$q$模拟应用于${}_{2} \phi_{1}$基本超几何级数的三项关系，推导出了一些基本的超几何恒等式，包括一些众所周知的和不太广为人知的恒等式。 显示英文摘要

摘要： In 2015, Ebisu presented a new method for finding hypergeometric identities based on three-term relations for the ${}_{2} F_{1}$ hypergeometric series. By using this method, he derived almost all of the previously known hypergeometric identities, as well as many new ones. In this paper, we derive several basic hypergeometric identities, including both well-known and not widely known ones, by applying a $q$-analogue of Ebisu's method to three-term relations for the ${}_{2} \phi_{1}$ basic hypergeometric series.