Growth of modified Painlevé transcendents of the fifth and the third kind

2004 ◽  
Vol 16 (2) ◽  
Author(s):  
Shun Shimomura
Keyword(s):  
Painlevé Transcendents ◽  
The Third ◽  
Painleve Transcendents

scholarly journals Equi-Distribution of Values for the Third and the Fifth Painlevé Transcendents

2008 ◽  
Vol 192 ◽  
pp. 89-109 ◽  
Author(s):  
Shun Shimomura
Keyword(s):  
Characteristic Function ◽  
Growth Order ◽  
Value Distribution Theory ◽  
Painlevé Transcendents ◽  
The Third ◽  
Domain Type ◽  
Distribution Of Values ◽  
Special Cases ◽  
Painleve Transcendents ◽  
Borel Exceptional Values

AbstractWe show equi-distribution properties of values for the third and the fifth Painlevé transcendents in a sectorial domain. For our purpose we define a characteristic function of sectorial domain type by employing value distribution theory in a half plane. Some special cases admit analogues of Borel exceptional values. Similar results are obtained for modified versions of these Painlevé transcendents, which are of infinite growth order.

The meromorphic nature of the sixth Painlevé transcendents

2004 ◽  
Vol 94 (1) ◽  
pp. 319-342 ◽  
Author(s):  
Aimo Hinkkanen ◽  
Ilpo Laine
Keyword(s):  
Painlevé Transcendents ◽  
Painleve Transcendents
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