Three-term relations between interpolation polynomials for a BCn-type basic hypergeometric series
Three-term relations between interpolation polynomials for a BCn-type basic hypergeometric series
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DOI：
10.1016/j.aim.2010.11.013
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发表时间：
2011-03
影响因子：
1.7
通讯作者：
Masahiko Ito
中科院分区：
文献类型：
--
作者：
Masahiko Ito
本文给出了一个BCn型杰克逊积分（q级数）所满足的n+1秩q-差分方程组的显式表达式，即一阶q-差分方程组的具体基.为此，我们引入两种类型的对称洛朗多项式称为插值多项式。插值多项式之间的三项关系在推导q-差分系统中起着至关重要的作用。作为应用，给出了Gustafson引入的q-积分乘积公式的另一种证明.
We present an explicit expression for the q-difference system of rank n+1 satisfied by a BCn-type Jackson integral (q-series) as first order simultaneous q-difference equations with a concrete basis. For this purpose we introduce two types of symmetric Laurent polynomials called the interpolation polynomials. Three-term relations between the interpolation polynomials play an essential role in deriving the q-difference system. As an application, we give another proof for the product formula of the q-integral introduced by Gustafson.