Some Implications of the WP-Bailey Tree

Some implications of the $2$-fold Bailey lemma

The $2$-fold Bailey lemma is a special case of the $s$-fold Bailey lemma introduced by Andrews in 2000. We examine this special case and its applications to partitions and recently discovered $q$-series identities. Our work provides a general comparison of the utility of the $2$-fold Bailey lemma and the more widely applied $1$-fold Bailey lemma. We also offer a discussion of the $spt_M(n)$ function and related identities.

General WP-Bailey Chains

Motivated by a recent paper of Liu and Ma, we describe a number of general WP-Bailey chains. We show that many of the existing WP-Bailey chains (or branches of the WP-Bailey tree), including chains found by Andrews, Warnaar and Liu and Ma, arise as special cases of these general WP-Bailey chains. We exhibit three new branches of the WP-Bailey tree, branches which also follow as special cases of these general WP-Bailey chains. Finally, we describe a number of new transformation formulae for basic hypergeometric series which arise as consequences of these new WP-Bailey chains.

WP - Bailey树及其应用

The WP - Bailey Tree and its Implications

我们的目标是一个彻底的分析WP-贝利树，最近扩展的经典贝利链。我们首先观察WP-贝利树如何自然地包含有限数量的经典q-超几何变换公式。然后，我们展示了如何超越这个闭集的结果，并在这个过程中，我们解释了迄今为止神秘的身份的D。布雷苏德其次，我们利用WP-Bailey对给出了A的最近公式的一个新的证明。基里洛夫最后，我们讨论了我们的方法和W。伯奇

Some implications of Chu's $_{10}ψ_{10}$ extension of Bailey's $_{6}ψ_{6}$ summation formula

Lucy Slater used Bailey's $_6ψ_6$ summation formula to derive the Bailey pairs she used to construct her famous list of 130 identities of the Rogers-Ramanujan type. In the present paper we apply the same techniques to Chu's $_{10}ψ_{10}$ generalization of Bailey's formula to produce quite general Bailey pairs. Slater's Bailey pairs are then recovered as special limiting cases of these more general pairs. In re-examining Slater's work, we find that her Bailey pairs are, for the most part, special cases of more general Bailey pairs containing one or more free parameters. Further, we also find ne…

$\rm A_2$ Bailey树与$\rm A_2^{(1)}$ Rogers-Ramanujan型恒等式

An $\mathrm{A}_2$ Bailey tree and $\mathrm{A}_2^{(1)}$ Rogers-Ramanujan-type identities

本研究将$\rm A_2$ Bailey链拓展为四参数$\rm A_2$ Bailey树，以此证明了Kanade-Russell猜想、Andrews-Gordon恒等式的$\rm A_2^{(1)}$类比及更一般的Rogers-Selberg型恒等式，推广了已有结果。