32 Painlevé TranscendentsProperties32.11 Asymptotic Approximations for Real Variables32.13 Reductions of Partial Differential Equations

§32.12 Asymptotic Approximations for Complex Variables

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Keywords:

Painlevé transcendents, asymptotic approximations, complex variables

Permalink:

http://dlmf.nist.gov/32.12

See also:

Annotations for Ch.32

Contents

1. §32.12(i) First Painlevé Equation
2. §32.12(ii) Second Painlevé Equation
3. §32.12(iii) Third Painlevé Equation

§32.12(i) First Painlevé Equation

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Permalink:

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

See also:

Annotations for §32.12 and Ch.32

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

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Permalink:

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

See also:

Annotations for §32.12 and Ch.32

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

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Keywords:

Painlevé transcendents, asymptotic approximations

Permalink:

http://dlmf.nist.gov/32.12.iii

See also:

Annotations for §32.12 and Ch.32

See Fokas et al. (2006, Chapter 16).

32.11 Asymptotic Approximations for Real Variables32.13 Reductions of Partial Differential Equations

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