Complex binomial theorem and pentagon identities
Abstract
We consider various pentagon identities realized by 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 Euler beta integral evaluation. 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 $$\omega_1+\omega_2\to 0$$ (or $$b\to i$$ in two-dimensional conformal field theory) applied to hyperbolic hypergeometric integrals.
Fields of Study & Subjects
Mathematics and Applications
Publication details
- Journal / source
- Theoretical and Mathematical Physics
- Publisher
- Pleiades Publishing Ltd
- Volume
- 226
- Issue
- 1
- Pages
- 1–20
- Publication date
- 1 January 2026
- Language
- EN