Derivatives of meromorphic functions and exponential functions |
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Authors: | Pai Yang Liangwen Liao Qiaoyu Chen |
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Affiliation: | 1. College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, China2. Department of Mathematics, Nanjing University, Nanjing 210093, China3. School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201620, China |
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Abstract: | We take up a new method to prove a Picard type theorem. Let f be a meromorphic function in the complex plane, whose zeros are multiple, and let R be a Möbius transformation. If ({overline {lim } _{r to infty }}frac{{Tleft( {r,f} right)}}{{{r^2}}} = infty ) then f′z) = R(e z ) has infinitely many solutions in the complex plane. |
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Keywords: | Meromorphic function quasinormal family Picard theorem |
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