title: Matsaev's theorem
text: # Matsaev's theorem
  
  Matsaev's theorem is a theorem from complex analysis, which characterizes the order and type of an entire function.
  
  The theorem was proven in 1960 by Vladimir Igorevich Matsaev.
  
  ## Matsaev's theorem
  
  Let $f(z)$ with $z=re^{i\theta }$ be an entire function which is bounded from below as follows
  
      $\log(|f(z)|)\geq -C{\frac {r^{\rho }}{|\sin(\theta )|^{s}}},$
  
  where
  
      $C>0,\quad \rho >1\quad$ and $\quad s\geq 0.$
  
  Then $f$ is of order $\rho$ and has finite type.
  
  