论文标题
无尽的beta积分
The Endless Beta Integrals
论文作者
论文摘要
我们考虑最通用的单变量高光beta积分不可分割的特殊变性限制$ω_1\ to -ω_2$（或$ b \ to {\ rm i} $）。该限制还应用于Euler-Gauss高几何函数的最通用双曲线类似物及其$ W（E_7）$的对称转换组。在与$ {\ rm sl}（2，\ mathbb {c}）$组相关的复数字段上，结果函数被识别为高几何函数。 FADDEEV模块化量子差异（或双曲γ函数）的新的类似类似的非平凡高几何变性在极限$ω_1\ toω_2$（或$ b \ f \ f \ to 1 $）中发现。
We consider a special degeneration limit $ω_1\to - ω_2$ (or $b\to {\rm i}$ in the context of $2d$ Liouville quantum field theory) for the most general univariate hyperbolic beta integral. This limit is also applied to the most general hyperbolic analogue of the Euler-Gauss hypergeometric function and its $W(E_7)$ group of symmetry transformations. Resulting functions are identified as hypergeometric functions over the field of complex numbers related to the ${\rm SL}(2,\mathbb{C})$ group. A new similar nontrivial hypergeometric degeneration of the Faddeev modular quantum dilogarithm (or hyperbolic gamma function) is discovered in the limit $ω_1\to ω_2$ (or $b\to 1$).
