论文标题
一类终止的关系$ {} _ 4f_3（4）$超几何系列
Relations for a class of terminating ${}_4F_3(4)$ hypergeometric series
论文作者
论文摘要
我们为特定类别的终止$ {} _ 4f_3（4）$超几何序列带有三个免费参数的关系。由这些关系组成的不变性组被证明是对称组$ s_3 $的同构。我们进一步研究终止$ {} _ 3f_2（4）$系列的关系，属于两个家庭。通过使用系列反转，我们检查了相应的终止$ {} _ 4f_3（1/4）$和$ {} _ 3f_2（1/4）$ series series关系。我们此外，我们还会得出几个非终止$ {} _ 3f_2（4）$和$ {} _ 3f_2（1/4）$系列的第一个$ n+1 $条款的总和。我们还展示了如何终止$ {} _ 2f_1（4）$和$ {} _ 3f_2（4）$系列的某些已知求和公式。
We derive relations for a certain class of terminating ${}_4F_3(4)$ 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 ${}_3F_2(4)$ series that fall under two families. By using a series reversal, we examine the corresponding terminating ${}_4F_3(1/4)$ and ${}_3F_2(1/4)$ series relations. We additionally derive formulas for the sums of the first $n+1$ terms of several nonterminating ${}_3F_2(4)$ and ${}_3F_2(1/4)$ series. We also show how certain known summation formulas for terminating ${}_2F_1(4)$ and ${}_3F_2(4)$ series follow as limiting cases of some of our relations.
