TY - JOUR
T1 - Growth of the first, the second and the fourth Painlevé transcendents
AU - Shimomura, Shun
PY - 2003/3
Y1 - 2003/3
N2 - For the first Painlevé equation, it is proved that every meromorphic solution satisfies T(r, w) = O(r5/2). In showing this estimate, we employ two types of auxiliary function, one of which is crucial in the proof of the Painlevé property. Our method is also applicable to the second (resp. the fourth) Painlevé transcendents, and we obtain T(r, w) = O(r3) (resp. O(r4)).
AB - For the first Painlevé equation, it is proved that every meromorphic solution satisfies T(r, w) = O(r5/2). In showing this estimate, we employ two types of auxiliary function, one of which is crucial in the proof of the Painlevé property. Our method is also applicable to the second (resp. the fourth) Painlevé transcendents, and we obtain T(r, w) = O(r3) (resp. O(r4)).
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U2 - 10.1017/S0305004102006400
DO - 10.1017/S0305004102006400
M3 - Article
AN - SCOPUS:0037365285
SN - 0305-0041
VL - 134
SP - 259
EP - 269
JO - Mathematical Proceedings of the Cambridge Philosophical Society
JF - Mathematical Proceedings of the Cambridge Philosophical Society
IS - 2
ER -