Barnes-Ismagilov Integrals and Hypergeometric Functions of the Complex Field

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2020
• 1. Verfasser: Neretin, Yury A.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2020
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/210776
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Barnes-Ismagilov Integrals and Hypergeometric Functions of the Complex Field. Yury A. Neretin. SIGMA 16 (2020), 072, 20 pages

We examine a family ₚ𝐺ᶜq[⁽ᵃ⁾₍b₎; 𝔃] of integrals of Mellin-Barnes type over the space ℤ × ℝ, such that functions 𝐺 naturally arise in the representation theory of the Lorentz group. We express ₚ𝐺ᶜq(𝔃) as quadratic expressions in the generalized hypergeometric functions ₚFq₋₁ and discuss further prop...