Value distribution of Painlevé transcendents of the fifth kind (Q1840591)

It is known that the set of fixed singular points of the fifth Painlevé equation (PV) is \(\{0,\infty\}\) and the solutions to (PV) are meromorphic on the universal covering surface of \(\mathbb{C}\setminus\{0\}\) where \(\mathbb{C}\) denotes the complex plane. By the transformation of the variable \(t= e^z\), the author obtains an equivalent equation \((\text{P}_{\text{E}})\) which solutions are meromorphic on the whole complex plane. Here, the author is concerned with \((\text{P}_{\text{E}})\) and gets a series of results on value distribution properties of the transcendental solutions to \((\text{P}_{\text{E}})\).