Complex binomial theorem and pentagon identities
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911412501086208 |
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| author | Belousov, N. M. Sarkissian, G. A. Spiridonov, V. P. |
| author_facet | Belousov, N. M. Sarkissian, G. A. Spiridonov, V. P. |
| contents | We consider different pentagon identities realized by the hyperbolic hypergeometric functions and investigate their degenerations to the level of complex hypergeometric functions. In particular, we show that one of the degenerations yields the complex binomial theorem which coincides with the Fourier transformation of the complex analogue of the Euler beta integral. At the bottom we obtain a Fourier transformation formula for the complex gamma function. This is done with the help of a new type of the limit $ω_1+ω_2\to 0$ (or $b\to \textrm{i}$ in two-dimensional conformal field theory) applied to the hyperbolic hypergeometric integrals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07562 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Complex binomial theorem and pentagon identities Belousov, N. M. Sarkissian, G. A. Spiridonov, V. P. Classical Analysis and ODEs High Energy Physics - Theory Mathematical Physics We consider different pentagon identities realized by the hyperbolic hypergeometric functions and investigate their degenerations to the level of complex hypergeometric functions. In particular, we show that one of the degenerations yields the complex binomial theorem which coincides with the Fourier transformation of the complex analogue of the Euler beta integral. At the bottom we obtain a Fourier transformation formula for the complex gamma function. This is done with the help of a new type of the limit $ω_1+ω_2\to 0$ (or $b\to \textrm{i}$ in two-dimensional conformal field theory) applied to the hyperbolic hypergeometric integrals. |
| title | Complex binomial theorem and pentagon identities |
| topic | Classical Analysis and ODEs High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2412.07562 |