From hyperbolic to complex Euler integrals
Classical Analysis and ODEs
2026-04-07 v1 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
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.
Cite
@article{arxiv.2604.04471,
title = {From hyperbolic to complex Euler integrals},
author = {N. M. Belousov and G. A. Sarkissian and V. P. Spiridonov},
journal= {arXiv preprint arXiv:2604.04471},
year = {2026}
}