Example 1.  The functions  [Graphics:Images/PainlevePropertyMod_gr_4.gif]  have singularities at the point  [Graphics:Images/PainlevePropertyMod_gr_5.gif].  
The functions  [Graphics:Images/PainlevePropertyMod_gr_6.gif]  have singularities at the point  [Graphics:Images/PainlevePropertyMod_gr_7.gif].  

Solution 1.

[Graphics:../Images/PainlevePropertyMod_gr_8.gif]

 

[Graphics:../Images/PainlevePropertyMod_gr_9.gif]

 

 

[Graphics:../Images/PainlevePropertyMod_gr_10.gif]

 

[Graphics:../Images/PainlevePropertyMod_gr_11.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2005