A note on the transcendency of Painlevé’s first transcendent
From MaRDI portal
Publication:3754314
DOI10.1017/S0027763000002762zbMath0613.34030OpenAlexW1493512061MaRDI QIDQ3754314
Publication date: 1988
Published in: Nagoya Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1017/s0027763000002762
second order differential equationPainlevé's first transcendentfirst order algebraic differential equations
Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Differential algebra (12H05) Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain (34M15)
Related Items
Coalescence limits for higher order Painlevé equations ⋮ Plane webs and Darboux polynomials ⋮ Differential algebraic function fields depending rationally on arbitrary constants ⋮ Hiroshi Umemura and French mathematics ⋮ Mathematical works of Hiroshi Umemura ⋮ Lie extensions ⋮ A classification of first order differential equations ⋮ Classical solutions of the third Painlevé equation ⋮ Irreducibility of Discrete Painlevé Equation of Type <i>D</i><sub>7</sub><sup>(1)</sup> ⋮ On algebraic relations between solutions of a generic Painlevé equation ⋮ Galoisian methods for testing irreducibility of order two nonlinear differential equations ⋮ Solutions of the second and fourth Painlevé equations, I ⋮ Dynamics on character varieties and Malgrange irreducibility of Painlevé VI equation ⋮ Irreducibility of the first Painlevé equation. ⋮ Painlevé equation PII and strongly normal extensions ⋮ Geometric characterization of strongly normal extensions ⋮ Painlevé's theorem on automorphic functions ⋮ Unnamed Item ⋮ Specialisation of the Galois groupoid of a vector field ⋮ Einstein-Weyl spaces and dispersionless Kadomtsev-Petviashvili equation from Painlevé I and II ⋮ Solutions of the third Painlevé equation I
Cites Work