论文标题
具有一个单位移位的超几何4F3的转换：一组理论研究
Transformations of the hypergeometric 4F3 with one unit shift: a group theoretic study
论文作者
论文摘要
我们研究了与参数的一个单位变化一起评估的4F3超几何函数的转换组。我们揭示了这个转型及其群体财产的一般形式。接下来，我们使用明确已知的转换来生成一个子组，然后对其结构进行彻底研究。使用3F2转换组的一些已知结果，我们表明该亚组是5度和5维整数晶格的对称组的直接乘积。我们研究了我们组的两项4F3转换与三项3F2变换之间的关系，并提出了一种计算在Unity评估的3F2函数的连续关系系数的方法。我们进一步提供了一类与我们小组要素相关的总和公式。在本文的附录中，我们给出了Wolfram Mathematica例程的集合，以促进小组计算。
We study the group of transformations of 4F3 hypergeometric functions evaluated at unity with one unit shift in parameters. We reveal the general form of this family of transformations and its group property. Next, we use explicitly known transformations to generate a subgroup whose structure is then thoroughly studied. Using some known results for 3F2 transformation groups, we show that this subgroup is isomorphic to the direct product of the symmetric group of degree 5 and 5-dimensional integer lattice. We investigate the relation between two-term 4F3 transformations from our group and three-term 3F2 transformations and present a method for computing the coefficients of the contiguous relations for 3F2 functions evaluated at unity. We further furnish a class of summation formulas associated with the elements of our group. In the appendix to this paper, we give a collection of Wolfram Mathematica routines facilitating the group calculations.
