Example 3
(a). The
functions
have poles at the point
.
Solution 3 (a).
![[Graphics:../Images/PainlevePropertyMod_gr_65.gif]](../Images/PainlevePropertyMod_gr_65.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_66.gif]](../Images/PainlevePropertyMod_gr_66.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_68.gif]](../Images/PainlevePropertyMod_gr_68.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_69.gif]](../Images/PainlevePropertyMod_gr_69.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_71.gif]](../Images/PainlevePropertyMod_gr_71.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_72.gif]](../Images/PainlevePropertyMod_gr_72.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_74.gif]](../Images/PainlevePropertyMod_gr_74.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_75.gif]](../Images/PainlevePropertyMod_gr_75.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_77.gif]](../Images/PainlevePropertyMod_gr_77.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_78.gif]](../Images/PainlevePropertyMod_gr_78.gif)
Remark 1. The
graphs of
look similar (in Red) because they have simple poles of order
.
Remark 2. The
graphs of
look similar (in Blue) because they have poles of order
.
(c) John H. Mathews 2005