Geodesic
Cercles de Remplissage and Asymptotic Behaviour
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 447-455

Voir la notice de l'article provenant de la source Cambridge University Press

In 1908, Lindelöf showed that if w = f(x) is a bounded holomorphic function in a sector S: |arg z| < θ 1, and if f(z) has an asymptotic value w 0 as z tends to ∞ along a half-ray in S; then f(z) tends uniformly to w 0 as z tends to ∞o within any sector |arg z| ≦ θ, 0 ≦ θ < θ 1. Montel (8) later replaced the condition that f(z) be bounded by the condition that f(z) be meromorphic and omitted three values. The following is an immediate consequence of the Lindelöf-Montel theorem.THEOREM 1. Let w = f(x) be a function meromorphic in the sector | arg z| < θ 1, and let f(z) tend to a value w 0 as z → ∞ along the positive real axis. 
Gauthier, Paul. Cercles de Remplissage and Asymptotic Behaviour. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 447-455. doi: 10.4153/CJM-1969-048-8
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