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 | |
【 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
【 预 览 】
Files | Size | Format | View |
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RO202106300000652ZK.pdf | 480KB | download |