On certain multiple Bailey, Rogers and Dougall type summation formulas
On certain multiple Bailey, Rogers and Dougall type summation formulas
复制标题
关于某些多重Bailey、Rogers和Dougall型求和公式
DOI：
10.2977/prims/1195145326
复制
发表时间：
1997
影响因子：
1.2
通讯作者：
J. F. van Diejen
中科院分区：
文献类型：
--
作者：
J. F. van Diejen
Bailey 的非常平衡的双边基本超几何 6 6 求和公式及其 Dougall 型 5H5 超几何退化的多维推广 q ！ 1 进行了研究。多重贝利和相当于与某些求和恒等式的非约简根系统的情况相对应的扩展，这些求和恒等式与最近由 Aomoto 和 Ito 猜想并由 Macdonald 证明的约简根系统有关。通过截断，我们获得了非常平衡的单边（基本）超几何 Rogers 6�5 和 Dougall 5F4 和（非终止和终止）的多维类似物。终止和可用于得出最近引入的几个变量的 (q-)Racah 多项式的范数的乘积公式。
A multidimensional generalization of Bailey's very-well-poised bi- lateral basic hypergeometric 6 6 summation formula and its Dougall type 5H5 hypergeometric degeneration for q ! 1 is studied. The multiple Bailey sum amounts to an extension corresponding to the case of a nonreduced root sys- tem of certain summation identities associated to the reduced root systems that were recently conjectured by Aomoto and Ito and proved by Macdonald. By truncation, we obtain multidimensional analogues of the very-well-poised unilateral (basic) hypergeometric Rogers 6�5 and Dougall 5F4 sums (both non- terminating and terminating). The terminating sums may be used to arrive at product formulas for the norms of recently introduced (q-)Racah polynomials in several variables.