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The analytic fixed point function II
Mots-clés :
Fixed point function, Coefficients, Bürmann-Lagrange, Asymptotics, Equilibrium, First return, Branching process, 2000 Mathematics Subject Classification, Primary: 30B10, Secondary: 60F99, 60J80 (en)Téléchargements
Abstract. Let ϕ be analytic in the unit disk ⅅ and let ϕ (ⅅ) ⊂ ⅅ, ϕ (0). Then w = ƶ/ϕ (ƶ) has an analytic inverse ƶ = ƒ (w) for w ϵ ⅅ, the fixed point function. This paper studies the case that ϕ (1) = ϕ'(1) = 1 with a growth condition for ϕ"(χ) and determines the asymptotic behaviour of various combinations of the coefficients of ϕ connected with ƒ. The results can be interpreted in various contexts of probability theory.
Références
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