论文标题
关于尾巴的身份
On Sum-Of-Tails Identities
论文作者
论文摘要
在本文中，获得了Andrews和Freitas的一般尾巴身份的有限类似物。我们得出了几个有趣的结果，因为这种类似物的特殊情况，特别是dixit，eyyyunni，maji和sood的最新身份。我们通过帮助Andrews，Garvan和Liang的尾巴标识，Ramanujan的身份以及两个新的结果以及Ramanujan的功能$σ（Q）$，另一个针对该功能和Ballantine介绍的功能。后来，我们引入了一个新的概括$ \ mathrm {ffw} _ {c}（n）$的fokkink，fokkink和wang的函数，并为其生成功能得出了身份。作为特殊情况，这给出了Andrews，Garvan和Liang给出的$ \ mathrm {spt}（n）$的生成功能的最新表示。我们还通过组合技术获得了一些加权分区身份，以及Ramanujan的两个三阶模拟theta函数的新表示形式。
In this article, a finite analogue of the generalized sum-of-tails identity of Andrews and Freitas is obtained. We derive several interesting results as special cases of this analogue, in particular, a recent identity of Dixit, Eyyyunni, Maji and Sood. We derive a new extension of Abel's lemma with the help of which we obtain a one-parameter generalization of a sum-of-tails identity of Andrews, Garvan and Liang, an identity of Ramanujan as well as two new results - one for Ramanujan's function $σ(q)$ and another for the function recently introduced by Andrews and Ballantine. Later we introduce a new generalization $\mathrm{FFW}_{c}(n)$ of a function of Fokkink, Fokkink and Wang and derive an identity for its generating function. This gives, as a special case, a recent representation for the generating function of $\mathrm{spt}(n)$ given by Andrews, Garvan and Liang. We also obtain some weighted partition identities along with new representations for two of Ramanujan's third order mock theta functions through combinatorial techniques.
