两个Saalschützian ${}_4F_3(1)$超几何级数线性组合的不变性群
An invariance group for a linear combination of two Saalschützian ${}_4F_3(1)$ hypergeometric series
摘要：
本文研究了一个函数$L(\vec{x})=L(a,b,c,d;e;f,g)$，它是两个萨尔许茨${}_4F_3(1)$超几何级数的线性组合.我们证明了一个基本的两项关系所满足的$L$功能，并表明，基本的两项关系意味着Coxeter组$W(D_5)$，它有1920个元素，是一个不变组$L(\vec{x})$。基于不变性群的双陪集分解，将$L(\vec{x})$的不变性关系分为六种类型。证明了基本的两项关系推广了关于超几何级数的经典结果。我们推导出了${}_3F_2(1)$级数的Reynae恒等式，终止Saalschützian ${}_4F_3(1)$级数的Bailey恒等式，以及Barnes的第二引理作为基本的两项关系的结果。
英文摘要：
We explore a function $L(\vec{x})=L(a,b,c,d;e;f,g)$ which is a linear combination of two Saalschützian ${}_4F_3(1)$ hypergeometric series. We demonstrate a fundamental two-term relation satisfied by the $L$ function and show that the fundamental two-term relation implies that the Coxeter group $W(D_5)$, which has 1920 elements, is an invariance group for $L(\vec{x})$. The invariance relations for $L(\vec{x})$ are classified into six types based on a double coset decomposition of the invariance group. The fundamental two-term relation is shown to generalize classical results about hypergeometric series. We derive Thomae's identity for ${}_3F_2(1)$ series, Bailey's identity for terminating Saalschützian ${}_4F_3(1)$ series, and Barnes' second lemma as consequences of the fundamental two-term relation.
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