Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 503-511

COMPLEX RICCATI DIFFERENTIAL EQUATIONS REVISITED

Norbert Steinmetz

Technische Universität Dortmund, Institut für Mathematik
D-44221 Dortmund, Germany; stein 'at' math.tu-dortmund.de

Abstract. We utilise a new approach via the so-called re-scaling method to derive a thorough theory for polynomial Riccati differential equations in the complex domain.

2010 Mathematics Subject Classification: Primary 30D30, 30D35, 30D45.

Key words: Riccati differential equation, Stokes sector, Stokes ray, asymptotic series, re-scaling, pole-free sector, Airy equation, Weber-Hermite equation.

Reference to this article: N. Steinmetz: Complex Riccati differential equations revisited. Ann. Acad. Sci. Fenn. Math. 39 (2014), 503-511.

Full document as PDF file

doi:10.5186/aasfm.2014.3929