On the Number of Poles of the First Painlev \’e Transcendents and Higher Order Anlogues

Let $w(z)$ be an arbitrary solution of the first Painleve equation (PI) $w’=6w^{2}+z$ . Then, $w(z)$ is atranscendental meromorphic function, and every pole is double. Denote by $n(r, w)$ the number of poles inside the circle $|z|<r$ . In this note, we prove the following: Theorem A. The growth order of $w(z)$ is not less than 5/2, namely (1) $\lim_{rarrow}\sup_{\infty}\frac{\log n(r,w)}{1\mathrm{o}\mathrm{g}r}\geq\frac{5}{2}$ . For another proof of this result, see [2]. It is known that the equations