On a family of integrals that extend the Askey-Wilson integral
On a family of integrals that extend the Askey-Wilson integral
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关于扩展 Askey-Wilson 积分的积分族
DOI：
10.1016/j.jmaa.2014.07.056
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发表时间：
2015
影响因子：
1.3
通讯作者：
N.S. Witte
中科院分区：
文献类型：
--
作者：
Masahiko Ito;N.S. Witte
我们研究了N= 2,3，…参数化的一类积分，推广了线性微分系统的保单变形的Q -类似理论和XXZ开量子自旋链的Baxter Q算子理论中出现的Askey-Wilson积分N= 2。这些积分是由Askey-Wilson权值的权重定义的矩的特殊例子，我们证明了这些积分是由我们构建的各种(N−1)-阶线性q差分方程表征的。此外，我们证明了这些积分可以计算为（N−1）B - C - 1型Jackson积分或φ 2 N+ 1 2 N+ 2基本超几何函数的有限和。
We study a family of integrals parameterised by N= 2, 3,… generalising the Askey–Wilson integral N= 2 which has arisen in the theory of q-analogs of monodromy preserving deformations of linear differential systems and in theory of the Baxter Q operator for the XXZ open quantum spin chain. These integrals are particular examples of moments defined by weights generalising the Askey–Wilson weight and we show the integrals are characterised by various (N− 1)-th order linear q-difference equations which we construct. In addition we demonstrate that these integrals can be evaluated as a finite sum of (N− 1) B C 1-type Jackson integrals or φ 2 N+ 1 2 N+ 2 basic hypergeometric functions.