We obtain a finite analogue of a recent generalization of an identity in Ramanujan's Notebooks. Differentiating it with respect to one of the parameters leads to a result whose limiting case gives a finite analogue of Andrews' famous identity for $\mathrm{\text{spt}}(n)$. The latter motivates us to extend the theory of the restricted partition function $p(n,N)$, namely, the number of partitions of n with largest parts less than or equal to N, by obtaining the finite analogues of rank and crank for vector partitions as well as of the rank and crank moments. As an application of the identity for our finite analogue of the spt-function, namely $\mathrm{\text{spt}}(n,N)$, we prove an inequality between the finite second rank and crank moments. The other results obtained include finite analogues of a recent identity of Garvan, an identity relating $d(n,N)$ and $\text{lpt}(n,N)$, namely the finite analogues of the divisor and largest parts functions respectively, and a finite analogue of the Beck-Chern theorem.

我们获得了Ramanujan的《笔记本》中恒等最近泛化的有限模拟。相对于其中一个参数进行微分会导致结果，其极限情况给出了安德鲁斯著名身份的有限模拟。$\mathrm{\text{spt}}（ñ）$。后者激励我们扩展受限分配函数的理论$p（ñ，ñ）$，即通过获得矢量分区的秩和曲柄以及秩和曲柄矩的有限类似物，最大部分小于或等于N的n个分区的数目。作为恒等式对spt函数的有限模拟的应用，即$\mathrm{\text{spt}}（ñ，ñ）$，我们证明了有限的第二等级和曲柄力矩之间的不等式。获得的其他结果包括Garvan最近身份的有限类似物，该身份与$d（ñ，ñ）$ 和 $\text{脂蛋白}（ñ，ñ）$，即除数和最大部分函数的有限类似物，以及Beck-Chern定理的有限类似物。