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arXiv 1901.04841math.NT
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提升Bailey偶到WP-Bailey偶

Lifting Bailey Pairs to WP-Bailey Pairs

James Mc Laughlin, Andrew V. Sills, Peter Zimmer

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24 pages
发表信息：
Discrete Mathematics 309 (2009), pp. 5077-5091
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摘要：

一对序列$(α_{n}(a,k,q),β_{n}(a,k,q))$，使得$α_0(a,k,q)=1$和\[ β_{n}(a,k,q) = \sum_{j=0}^{n} \frac{(k/a; q)_{n-j}(k; q)_{n+j}}{(q;q)_{n-j}(aq;q)_{n+j}}α_{j}(a,k,q) \]被称为\emph{WP-Bailey Pair}。在这样一对中设置$k=0$后，我们得到一个\emph{Bailey pair}。本文考虑将Bailey对“提升”为WP-Bailey对的问题，并利用由此得到的一些新的WP-Bailey对导出了基本超几何级数与新的Rogers-Ramanujan-Slater型单和与双和恒等式之间的一些新恒等式.

英文摘要：

A pair of sequences $(α_{n}(a,k,q),β_{n}(a,k,q))$ such that $α_0(a,k,q)=1$ and \[ β_{n}(a,k,q) = \sum_{j=0}^{n} \frac{(k/a; q)_{n-j}(k; q)_{n+j}}{(q;q)_{n-j}(aq;q)_{n+j}}α_{j}(a,k,q) \] is termed a \emph{WP-Bailey Pair}. Upon setting $k=0$ in such a pair we obtain a \emph{Bailey pair}. In the present paper we consider the problem of "lifting" a Bailey pair to a WP-Bailey pair, and use some of the new WP-Bailey pairs found in this way to derive some new identities between basic hypergeometric series and new single sum- and double sum identities of the Rogers-Ramanujan-Slater type.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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