Theorem 5.1 (The exponential function).  The function  [Graphics:Images/ComplexFunExponentialMod_gr_14.gif]  is an entire function satisfying the following conditions:

(ii).   [Graphics:Images/ComplexFunExponentialMod_gr_17.gif],   i.e.   [Graphics:Images/ComplexFunExponentialMod_gr_18.gif].  

Demonstration for Theorem 5.1 (ii).

[Graphics:../Images/ComplexFunExponentialMod_gr_57.gif]





[Graphics:../Images/ComplexFunExponentialMod_gr_58.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) 2006 John H. Mathews, Russell W. Howell