F⁡(a+λ,b-λc;12-12⁢z)=2(a+b-1)/2⁢(z+1)(c-a-b-1)/2(z-1)c/2⁢ζ⁢sinh⁡ζ⁢(λ+12⁢a-12⁢b)1-c⁢(Ic-1⁡((λ+12⁢a-12⁢b)⁢ζ)⁢(1+O⁡(λ-2))+Ic-2⁡((λ+12⁢a-12⁢b)⁢ζ)2⁢λ+a-b⁢((c-12)⁢(c-32)⁢(1ζ-coth⁡ζ)+12⁢(2⁢c-a-b-1)⁢(a+b-1)⁢tanh⁡(12⁢ζ)+O⁡(λ-2))),