Value distribution of the third Painlevé transcendents in sectorial domains
Yoshikatsu Sasaki
Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 83, Number 6
(2007), 79-82.
Abstract
This article concerns the value distribution of the third Painlevé transcendents in sectorial domains around fixed singular points. We show that the cardinality of the zeros of a third Painlevé transcendent in a sector has an asymptotic growth of finite order, thereby giving an improvement of the known estimation.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.pja/1188405575
Digital Object Identifier: doi:10.3792/pjaa.83.79
Mathematical Reviews number (MathSciNet): MR2355502
References
Y. Sasaki, Value distribution of the fifth Painlevé transcendents in sectorial domains, J. Math. Anal. Appl. 330 (2007), 817--828. (in press).
Mathematical Reviews (MathSciNet): MR2308409
Digital Object Identifier: doi:10.1016/j.jmaa.2006.07.083
Y. Sasaki, Construction of the auxiliary functions %%!! for the value distribution of the fifth Painlevé transcendents in sectorial domains, RIMS Kôkyûroku Bessatsu B2 (2007), 209--214.
Mathematical Reviews (MathSciNet): MR2310031
S. Shimomura, Growth of modified Painlevé transcendents of the fifth and the third kind, Forum Math. 16 (2004), 231--247.
Mathematical Reviews (MathSciNet): MR2039098
Digital Object Identifier: doi:10.1515/form.2004.011
S. Shimomura, Value distribution of Painlevé transcendents of the third kind, Complex Variables Theory Appl. 40 (1999), no. 1, 51--62.
Mathematical Reviews (MathSciNet): MR1742870
H. Umemura and H. Watanabe, Solutions of the third Painlevé equation. I, Nagoya Math. J. 151 (1998), 1--24.
Mathematical Reviews (MathSciNet): MR1650348
Project Euclid: euclid.nmj/1118766573
Proceedings of the Japan Academy, Series A, Mathematical Sciences
