arXiv subjects

N. M. Belousov

Publications and source records attributed to N. M. Belousov.

3 recordsLinked to original sources

arXiv2026

From hyperbolic to complex Euler integrals

Hyperbolic hypergeometric integrals are defined as Barnes-type integrals of products of hyperbolic gamma functions. Their reduction to ordinary hypergeometric functions is well known. We study in detail their degeneration to complex hypergeometric functions. Namely, using uniform bounds on the integrands, we prove that the univariate hyperbolic beta integral and the conical function degenerate to two-dimensional integrals over the complex plane.

math.CA↗

arXiv2025

Complex binomial theorem and pentagon identities

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.

math.CA↗

arXiv2025

Complex rational Ruijsenaars model. The two-particle case

We consider a complex rational degeneration of the hyperbolic Ruijsenaars model emerging in the limit $ω_1+ω_2\to 0$ (or $b\to \imath$ in $2d$ CFT) and investigate in detail the two-particle case. Corresponding wave functions are described by complex hypergeometric functions in the Mellin-Barnes representation. Their dual integral representation and reflection symmetry in the coupling constant are established. Besides, a complex limit of the hyperbolic Baxter $Q$-operators is considered. Another complex degeneration of the hyperbolic Ruijsenaars model is obtained by taking a special $ω_1-ω_2\to 0$ (or $b\to 1$) limit. Additionally, two new degenerations to the complex Calogero-Sutherland type models are described.

math-ph↗