scholarly journals Value distribution of the third Painlevé transcendents in sectorial domains

2007 ◽  
Vol 83 (6) ◽  
pp. 79-82 ◽  
Author(s):  
Yoshikatsu Sasaki
Keyword(s):  
Value Distribution ◽  
Painlevé Transcendents ◽  
The Third ◽  
Painleve Transcendents ◽  
Sectorial Domains

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.

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