Ilim ha’m ja’miyet 5-1-сан (2026) · 9-11-беттер
CONFORMAL MAPPING ONTO THE EXTERIOR OF A REGULAR TRIANGLE
Kalbaev, Sultanbek Nazerbaevich, Jaksibaev, Sultanbek Amangeldi ulı, Kalbaev, Sultanbek Nazerbaevich, Jaksibaev, Sultanbek Amangeldi ulı, Калбаев, Султанбек Назербаевич, Джаксыбаев, Султанбек Амангельдиевич
Аннотация
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.
konform akslantirishKristoffel-Shvars integralimuntazam uchburchaksohaning tashqi ko‘rinishilogarifmik sig‘imkonform radiustransfinit diametrgamma-funksiyakompleks tekislikideal suyuqlik oqimi
Метадайындар булагы: журналдын OAI-PMH архиви · Sindex толук текстти сактабайт, булакка шилтеме берет.