Infinite families of Hecke-Rogers type series and their truncated representations
Infinite families of Hecke-Rogers type series and their truncated representations
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DOI：
10.1016/j.aam.2021.102310
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发表时间：
2022-06
期刊：
影响因子：
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通讯作者：
Ernest X. W. Xia
中科院分区：
文献类型：
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作者：
Ernest X. W. Xia
摘要最近，Andrews和Merca研究了Euler五角数定理的截断形式。他们的工作开启了对截断级数的新研究。从那时起，人们发现了许多截短版本的theta系列。最近，Wang和Yee将截断级数的研究推广到Hecke-Rogers型级数，得到了三个新的截断Hecke-Rogers级数。受这些工作的启发，我们不仅证明了几个Hecke-Rogers型级数的无限族及其截断形式，而且在一些有趣的配分函数上建立了一些不等式。特别地，我们推广了Wang和Yee以及He的一些结果。我们的工作主要依赖于某些可终止的基本超几何ϕ2~3级数的计算公式。
Abstract Recently, Andrews and Merca studied the truncated version of Euler's pentagonal number theorem. Their work opened up a new study on truncated series. Since then, many truncated versions of theta series have been discovered. Very recently, Wang and Yee generalized the study on truncated series to Hecke-Rogers type series and obtained three new truncated Hecke-Rogers series. Inspired by these works, we not only prove several infinite families of Hecke-Rogers type series and their truncated versions, but also establish some inequalities on some interesting partition functions in this paper. In particular, we generalize some results due to Wang and Yee, and He. Our work mainly relies on some formulas on the evaluation of certain terminating basic hypergeometric ϕ 2 3 series.