论文标题
在刘的扩展公式上
On an expansion formula of Liu
论文作者
论文摘要
在本文中，我们将LIU的扩展公式扩展到了root System $ a_ {n}的多个基本高几幅序列。我们首先在root System $ a_ {n} $上建立一个非常通用的多个扩展公式，然后推断出Liu扩展公式的几个$ a_ {n} $扩展。从这些多个公式中，我们得出了两组无限产品的多个膨胀公式。作为应用程序，我们推断出$ a_ {n} $ rogers的$ \ text {} _ {6} ϕ_ {5} $ summation，$ a_ {n} $ sylvester的身份的扩展，某些多重扩展公式$（q）_ {\ infty}^{m}，\ text {\ ensureMath {π_{q}}} $和$ 1/π_{q} $，两个$ a_ {n} $ extermentity of a_ a_ a_ a_ a_ a_ { $ _ {6} ϕ_ {5} $ summation，$ a_ {n} $扩展方的fang的标识和$ a_ {n} $扩展Andrews扩展公式。
In this paper, we extend an expansion formula of Liu to multiple basic hypergeometric series over the root system $A_{n}.$ The usefulness of Liu's expansion formula in special functions and number theory has been shown by Liu and many others. We first establish a very general multiple expansion formula over the root system $A_{n}$ and then deduce several $A_{n}$ extensions of Liu's expansion formula. From these multiple formulas, we derive two groups of multiple expansion formulas for infinite products. As applications, we deduce an $A_{n}$ Rogers' $\text{}_{6}ϕ_{5}$ summation, an $A_{n}$ extension of Sylvester's identity, some multiple expansion formulas for $(q)_{\infty}^{m},\text{\ensuremath{π_{q}}}$ and $1/π_{q}$, two $A_{n}$ extensions of the Rogers-Fine identity, an $A_{n}$ extension of Liu's extension of Rogers' non-terminating $_{6}ϕ_{5}$ summation, an $A_{n}$ extension of a generalization of Fang's identity and an $A_{n}$ extension of Andrews' expansion formula.
