TY  - JOUR
ID  - Parusnikova2014
LB  - Parusnikova2014
AU  - Parusnikova, Anastasia V.
TI  - On Gevrey orders of formal power series solutions to the third and fifth Painlevé equations near infinity
ST  - On Gevrey orders of formal power series solutions to the third and fifth Painlevé equations near infinity
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2014
VL  - 34
IS  - 3
SP  - 591
EP  - 599
DO  - http://dx.doi.org/10.7494/OpMath.2014.34.3.591
UR  - http://dx.doi.org/10.7494/OpMath.2014.34.3.591
AB  - The question under consideration is Gevrey summability of formal power series solutions to the third and fifth Painlevé equations near infinity. We consider the fifth Painlevé equation in two cases: when \(\alpha\beta\gamma\delta \neq 0\) and when \(\alpha\beta\gamma \neq 0\), \(\delta =0\) and the third Painlevé equation when all the parameters of the equation are not equal to zero. In the paper we prove Gevrey summability of the formal solutions to the fifth Painlevé equation and to the third Painlevé equation, respectively.
KW  - Painlevé equations
KW  - Newton polygon
KW  - asymptotic expansions
KW  - Gevrey orders
SN  - 1232-9274
ER  -