We derive relations for a certain class of terminating ${}_4{F}_3(4)$ hypergeometric series with three free parameters. The invariance group composed of these relations is shown to be isomorphic to the symmetric group $S_3$. We further study relations for terminating ${}_3{F}_2(4)$ series that fall under two families. By using a series reversal, we examine the corresponding terminating ${}_4{F}_3(1/4)$ and ${}_3{F}_2(1/4)$ series relations. We additionally derive formulas for the sums of the first n + 1 terms of several nonterminating ${}_3{F}_2(4)$ and ${}_3{F}_2(1/4)$ series. We also show how certain known summation formulas for terminating ${}_2{F}_1(4)$ and ${}_3{F}_2(4)$ series follow as limiting cases of some of our relations.

我们为某一类终止派生关系${}_4{F}_3(4)$具有三个自由参数的超几何级数。由这些关系组成的不变群同构于对称群${\mathrm{小号}}_3$. 我们进一步研究终止关系${}_3{F}_2(4)$属于两个家庭的系列。通过使用系列反转，我们检查相应的终止${}_4{F}_3(1/4)$和${}_3{F}_2(1/4)$系列关系。我们还推导出 几个非终止项的前n + 1 项之和的公式${}_3{F}_2(4)$和${}_3{F}_2(1/4)$系列。我们还展示了某些已知的求和公式如何终止${}_2{F}_1(4)$和${}_3{F}_2(4)$系列遵循作为我们的一些关系的限制情况。