§32.12 Asymptotic Approximations for Complex Variables

Keywords:: Painlevé transcendents
Permalink:: http://dlmf.nist.gov/32.12

Contents

§32.12(i) First Painlevé Equation
§32.12(ii) Second Painlevé Equation
§32.12(iii) Third Painlevé Equation

§32.12(i) First Painlevé Equation

Permalink:: http://dlmf.nist.gov/32.12.i

See Boutroux (1913), Kapaev and Kitaev (1993), Takei (1995), Costin (1999), Joshi and Kitaev (2001), Kapaev (2004), and Olde Daalhuis (2005b).

§32.12(ii) Second Painlevé Equation

Permalink:: http://dlmf.nist.gov/32.12.ii

See Boutroux (1913), Novokshënov (1990), Kapaev (1991), Joshi and Kruskal (1992), Kitaev (1994), Its and Kapaev (2003), and Fokas et al. (2006, Chapter 7).

§32.12(iii) Third Painlevé Equation

Keywords:: Painlevé transcendents
Permalink:: http://dlmf.nist.gov/32.12.iii

See Fokas et al. (2006, Chapter 16).