Derivatives of meromorphic functions and exponential functions

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 {{\displaystyle \overline{\lim }}}_{r\to \infty }{\displaystyle \frac{T(r,f)}{r^{\mathrm{2}}}}=\infty \mathrm{then}{f}^{\text{'}}(z)=R(e^z) has infinitely many solutions in the complex plane.

Keywords

Meromorphic function / quasinormal family / Picard theorem

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