DURÍS ÚShMÚYEShLIKTIŃ SÍRTQÍ OBLASTÍNA KONFORM SÁWLELENDIRIW
Avtorlar
Gilt sózler: conformal represcuting, Christoffel–Schwarz integral, regular triangle, exterior domain, logarithmic capacity, conformal radius, transfinite diameter, gamma function, complex plane, ideal fluid flow, potential theory
Annotaciya
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.
Paydalanılǵan ádebiyatlar
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