Geodesic
Global Meromorphy of Solutions of the Painlev\'e Equations and Their Hierarchies
Informatics and Automation, Analysis and mathematical physics, Tome 311 (2020), pp. 106-122

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We show that all local holomorphic solutions of all equations constituting the hierarchies of the first and second Painlevé equations can be analytically continued to meromorphic functions on the whole complex plane. We also present a new conceptual proof of the fact that all local holomorphic solutions of the first, second, and fourth Painlevé equations are globally meromorphic.
Keywords: meromorphic function, hierarchies of Painlevé equations, analytic continuation. 
@article{TRSPY_2020_311_a5,
     author = {A. V. Domrin and B. I. Suleimanov and M. A. Shumkin},
     title = {Global {Meromorphy} of {Solutions} of the {Painlev\'e} {Equations} and {Their} {Hierarchies}},
     journal = {Informatics and Automation},
     pages = {106--122},
     publisher = {mathdoc},
     volume = {311},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2020_311_a5/}
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A. V. Domrin; B. I. Suleimanov; M. A. Shumkin. Global Meromorphy of Solutions of the Painlev\'e Equations and Their Hierarchies. Informatics and Automation, Analysis and mathematical physics, Tome 311 (2020), pp. 106-122. http://geodesic.mathdoc.fr/item/TRSPY_2020_311_a5/