The first, the second and the fourth Painlevé transcendents are of finite order.

DOI10.3792/PJAA.77.42zbMath1097.34065OpenAlexW2053487750MaRDI QIDQ5945219

Shun Shimomura

Publication date: 2001

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.pja/1148393109

zbMATH Keywords

Painlevé equationsgrowth order

Mathematics Subject Classification ID

Value distribution of meromorphic functions of one complex variable, Nevanlinna theory (30D35) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55)

Related Items (8)

Airy solutions of Painlevé's second equation ⋮ Estimates of the proximate function of differential polynomials ⋮ Equi-Distribution of Values for the Third and the Fifth Painlevé Transcendents ⋮ Special polynomials associated with rational solutions of the Painlevé equations and applications to soliton equations ⋮ Value Distribution and Growth of Solutions of Certain Painlevé Equations ⋮ Transcendental Meromorphic Solutions of P 34 and Small Targets ⋮ Meromorphic solutions of P_4,34 and their value distribution ⋮ Painlevé σ-equations S1, S2, S4 and their value distribution

Cites Work

• Nevanlinna theory and complex differential equations
• Growth of the first, the second and the fourth Painlevé transcendents
• Solutions of the first and second Painlevé equations are meromorphic
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