For a solution y(x) of the fifth (resp. third) Painlevé equation, the function w(z) = y(ez) is meromorphic in ℂ. It is proved that T(r, w)=O(eΛr) (resp. O(eΛr)), where Λ (resp. Λ) is some positive number independent of w(z). Moreover, using this result, we estimate the proximity functions m(r, w), m(r, 1/(w-c)) (cℂ).
ASJC Scopus subject areas
- Applied Mathematics