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Functions of Finite Logarithmic Order in the Unit Disc, Part II

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Part I of this paper illustrates how the concept of logarithmic order in the unit disc, defined in terms of the Nevanlinna characteristic, gives a natural growth scale for meromorphic functions of unbounded characteristic but of zero (usual) order of growth. Part II deals with the analytic case, where the logarithmic order can be defined in terms of the maximum modulus as well as in terms of Wiman–Valiron indices. Given an analytic function \(f\), these logarithmic orders are related to the Taylor coefficients of \(f\). Part II culminates in revealing a refinement of Wiman–Valiron theory.

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The authors would like to thank the reviewer for making suggestions for improving the paper.

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Correspondence to Zhi-Tao Wen.

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Communicated by Stephan Ruscheweyh.

This research was supported in part by the Academy of Finland #268009 and by the China Scholarship Council (CSC).

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Heittokangas, J., Wen, ZT. Functions of Finite Logarithmic Order in the Unit Disc, Part II. Comput. Methods Funct. Theory 15, 37–58 (2015).

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