论文标题
广义基本超几何功能的产品总和的新身份
A new identity for the sum of products of generalized basic hypergeometric functions
论文作者
论文摘要
我们证明了通用基本高几何功能的二元性关系。它构成了第二名和第三名作者的最新结果的$ q $ - 概括，并概括了第三名命名作者（共同与冯和杨共同使用）以及Heine的$ {} _ 2dcisto {1} _ {1} $由于suzuki造成的功能的近期身份。我们进一步探讨了我们的身份的各种后果，导致终止和非终止通用基本高几幅体系列可能是几个新的多期关系。此外，我们提供了结果的汇合版本，并提供了许多明确的例子。
We prove a duality relation for generalized basic hypergeometric functions. It forms a $q$-extension of a recent result of the second and the third named authors and generalizes both a $q$-hypergeometric identity due to the third named author (jointly with Feng and Yang) and a recent identity for the Heine's ${}_2ϕ_{1}$ function due to Suzuki. We further explore various consequences of our identity leading to several presumably new multi-term relations for both terminating and non-terminating generalized basic hypergeometric series. Moreover, we give confluent versions of our results and furnish a number of explicit examples.
