DURÍS ÚShMÚYEShLIKTIŃ SÍRTQÍ OBLASTÍNA KONFORM SÁWLELENDIRIW - Kalbaev, Sultanbek Nazerbaevich; Jaksibaev, Sultanbek Amangeldi ulı (ILIM hám JÁMIYET, 2026)
This article considers the conformal mapping of the exterior of the unit disk (the domain |z|>1) onto the exterior (unbounded) domain of a regular triangle. The mapping function is derived using the exterior form of the Christoffel–Schwarz integral, expanded into a power series, and its properties are analysed. It is shown that the logarithmic capacity (conformal radius) of the triangle is expressed through the transcendental constant Γ(1/3): R/C = 2/3 B(2/3,2/3) = 8π²/3Γ(1/3)³ ≈ 1.3689. As a physical application, the ideal fluid flow past the triangle is illustrated. The study employs methods of the geometric theory of functions of a complex variable, the Christoffel–Schwarz integral, series expansion, and computer visualization.