Digital Library of Mathematical Functions
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32 Painlevé TranscendentsProperties

§32.5 Integral Equations

Let K(z,ζ) be the solution of

32.5.1 K(z,ζ)=kAi(z+ζ2)+k24zzK(z,s)Ai(s+t2)Ai(t+ζ2)st,

where k is a real constant, and Ai(z) is defined in §9.2. Then

32.5.2 w(z)=K(z,z),

satisfies PII with α=0 and the boundary condition

32.5.3 w(z)kAi(z),
z+.