$q$ -差分方程与Roger-Ramanujan-Bailey型恒等式
$q$-Difference Equations and Identities of the Rogers--Ramanujan--Bailey Type
摘要：
在最近的一篇论文中，我定义了“标准多参数贝利对”（SMPBP），并证明了W.N.贝利在他的著名论文（\textit{Proc. London Math. Soc. (2)}，\textbf{50}（1948），1- 10）中作为SMPBP的特例出现。此外，我还发现了一些新的罗杰斯-拉马努金类型的身份。从一个给定的贝利对，通常只有一个或两个罗杰斯-拉马努金类型的身份立即遵循。本文给出了与SMPBP相联系的$q$ -差分方程，并利用这些$q$ -差分方程推导了完整的Rogers-Ramanujan型恒等式族.
英文摘要：
In a recent paper, I defined the "standard multiparameter Bailey pair" (SMPBP) and demonstrated that all of the classical Bailey pairs considered by W.N. Bailey in his famous paper (\textit{Proc. London Math. Soc. (2)}, \textbf{50} (1948), 1--10) arose as special cases of the SMPBP. Additionally, I was able to find a number of new Rogers-Ramanujan type identities. From a given Bailey pair, normally only one or two Rogers-Ramanujan type identities follow immediately. In this present work, I present the set of $q$-difference equations associated with the SMPBP, and use these $q$-difference equations to deduce the complete families of Rogers-Ramanujan type identities.
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