期刊论文详细信息
Symmetry Integrability and Geometry-Methods and Applications
The Endless Beta Integrals
article
Gor A. Sarkissian1  Vyacheslav P. Spiridonov2 
[1] Laboratory of Theoretical Physics;Department of Physics, Yerevan State University
关键词: elliptic hypergeometric functions;    complex gamma function;    beta integrals;    startriangle relation;   
DOI  :  10.3842/SIGMA.2020.074
来源: National Academy of Science of Ukraine
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【 摘 要 】

We consider a special degeneration limit $\omega_1\to - \omega_2$ (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 $\omega_1\to \omega_2$ (or $b\to 1$).

【 授权许可】

Unknown   

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