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Asymptotic series and algebroid functions

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Titel:	Asymptotic series and algebroid functions
Autoren:	Levin, B. Ya., Ronkin, A. L.
Verlagsinformationen:	American Mathematical Society (AMS), Providence, RI
Schlagwörter:	Asymptotic representations in the complex plane, Ritt theorems, meromorphic functions, algebroidal function, Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable, quasi- polynomial, Entire and meromorphic functions of one complex variable, and related topics
Beschreibung:	The main result of this very saturated note is the following theorem. Let the coefficients \(P_{\ell}(z)\) of the equation \[ (1)\quad P_ 0(z)w^ n+P_ 1(z)w^{n-1}+...+P_ n(z)=0 \] admit in an angle \(S_{\beta}\equiv S_{0,\beta}\), \(S_{\phi,\beta}=\{z:\) \(\| \arg z- \phi \| \pi)\) and let the set \(\{\lambda_{j\ell}\}\) be separated. Then for some \(\alpha
Publikationsart:	Article
Dateibeschreibung:	application/xml
Zugangs-URL:	https://zbmath.org/3959888
Dokumentencode:	edsair.c2b0b933574d..3c36b30b02bee67ea5fd2d17d3d2fbc4
Datenbank:	OpenAIRE

Beschreibung
Abstract:	The main result of this very saturated note is the following theorem. Let the coefficients \(P_{\ell}(z)\) of the equation \[ (1)\quad P_ 0(z)w^ n+P_ 1(z)w^{n-1}+...+P_ n(z)=0 \] admit in an angle \(S_{\beta}\equiv S_{0,\beta}\), \(S_{\phi,\beta}=\{z:\) \(\| \arg z- \phi \| \pi)\) and let the set \(\{\lambda_{j\ell}\}\) be separated. Then for some \(\alpha