Geodesic
On Convergent Series Expansions of Solutions of the Riccati Equation
Matematičeskie zametki, Tome 105 (2019) no. 4, pp. 603-615.

Voir la notice de l'article provenant de la source Math-Net.Ru

The Riccati equation with coefficients expandable in convergent power series in a neighborhood of infinity are considered. Extendable solutions of such equations are studied. Methods of power geometry are used to obtain conditions for convergent series expansions of these solutions. An algorithm for deriving such series is given.
Mots-clés : Riccati equation
Keywords: extendable solution, power geometry, Newton polygon, asymptotic expansion. 
@article{MZM_2019_105_4_a10,
     author = {V. S. Samovol},
     title = {On {Convergent} {Series} {Expansions} of {Solutions} of the {Riccati} {Equation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {603--615},
     publisher = {mathdoc},
     volume = {105},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_105_4_a10/}
}
TY  - JOUR
AU  - V. S. Samovol
TI  - On Convergent Series Expansions of Solutions of the Riccati Equation
JO  - Matematičeskie zametki
PY  - 2019
SP  - 603
EP  - 615
VL  - 105
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2019_105_4_a10/
LA  - ru
ID  - MZM_2019_105_4_a10
ER  - 
%0 Journal Article
%A V. S. Samovol
%T On Convergent Series Expansions of Solutions of the Riccati Equation
%J Matematičeskie zametki
%D 2019
%P 603-615
%V 105
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2019_105_4_a10/
%G ru
%F MZM_2019_105_4_a10
V. S. Samovol. On Convergent Series Expansions of Solutions of the Riccati Equation. Matematičeskie zametki, Tome 105 (2019) no. 4, pp. 603-615. http://geodesic.mathdoc.fr/item/MZM_2019_105_4_a10/

[1] J. Riccati, “Animadversationes in aequationes differentiales secundi gradus”, Acta Erud. Suppl., 8 (1724), 66–73

[2] G. N. Vatson, Teoriya besselevykh funktsii, Ch. 1, IL, M., 1949 | MR | Zbl

[3] E. Kamke, Spravochnik po obyknovennym differentsialnym uravneniyam, Nauka, M., 1961 | MR | Zbl

[4] A. D. Bryuno, “Asimptotiki i razlozheniya reshenii obyknovennogo differentsialnogo uravneniya”, UMN, 59:3 (357) (2004), 31–80 | DOI | MR | Zbl

[5] A. D. Bryuno, “Slozhnye razlozheniya reshenii obyknovennogo differentsianogo uravneniya”, Dokl. AN, 406:6 (2006), 730–733 | MR

[6] V. S. Samovol, “Asimptoticheskoe integrirovanie uravneniya Rikkati metodami stepennoi geometrii”, Dokl. AN, 475:5 (2017), 496–499 | MR | Zbl

[7] V. V. Palin, E. V. Radkevich, “O povedenii stabiliziruyuschikhsya reshenii dlya uravneniya Rikkati”, Tr. sem. im. I. G. Petrovskogo, 31, Izd-vo Mosk. un-ta, M., 2016, 110–133