Parusnikova, A.Vasilyev, A.2019-09-082019-09-082019-09-082019-10-0110.1007/s10883-019-09449-2https://infoscience.epfl.ch/handle/20.500.14299/160945WOS:000482390700010In this paper, we study the third Painleve equation with parameters gamma = 0, alpha delta not equal 0. The Puiseux series formally satisfying this equation (after a certain change of variables) asymptotically approximate of Gevrey order one solutions to this equation in sectors with vertices at infinity. We present a family of values of the parameters delta = -beta(2)/2 not equal 0 such that these series are of exact Gevrey order one, and hence diverge. We prove the 1-summability of them and provide analytic functions which are approximated of Gevrey order one by these series in sectors with the vertices at infinity.Automation & Control SystemsMathematics, AppliedMathematicspainleve equationsasymptotic expansionssummability34m2534m3034m55text::journal::journal article::research article