论文标题
Bhoria，Eyyunni和Maji及其应用
A finite analogue of a $q$-series identity of Bhoria, Eyyunni and Maji and its applications
论文作者
论文摘要
Bhoria，Eyyunni和Maji最近获得了四参数$ Q $ series的身份，不仅在他的第二个笔记本的第354和355页上，不仅可以作为特殊情况，而且还提供了他的第二个笔记本的所有五个条目，而且还允许他们获得Bressoud和Subbarao的分析证明。在这里，我们获得了其身份的有限类似物，自然会提供Ramanujan结果的有限类似物。使用这些有限类似物之一，我们将涉及$ {} _ 2ϕ_1 $的有限总和的身份推断出身份。然后，将此身份应用于获得安德鲁斯（Andrews）著名身份的生成函数版本的概括，以$ \ textup {spt}（n）$。 $ q $ - 系列$ \ sum_ {n = 1}^{\ infty} \ textup {spt}（n）q^n $与$ s（z，q）$完全不同。给出了我们身份的进一步应用。最后，我们概括了Andrews，Chan和Kim的结果，其中涉及排名和曲柄的第一个奇数时刻。
Bhoria, Eyyunni and Maji recently obtained a four-parameter $q$-series identity which gives as special cases not only all five entries of Ramanujan on pages 354 and 355 of his second notebook but also allows them to obtain an analytical proof of a result of Bressoud and Subbarao. Here, we obtain a finite analogue of their identity which naturally gives finite analogues of Ramanujan's results. Using one of these finite analogues, we deduce an identity for a finite sum involving a ${}_2ϕ_1$. This identity is then applied to obtain a generalization of the generating function version of Andrews' famous identity for the smallest parts function $\textup{spt}(n)$. The $q$-series which generalizes $\sum_{n=1}^{\infty}\textup{spt}(n)q^n$ is completely different from $S(z, q)$ considered by Andrews, Garvan and Liang. Further applications of our identity are given. Lastly we generalize a result of Andrews, Chan and Kim which involves the first odd moments of rank and crank.
