F⁡(a,b;c;z)=∑s=0∞(a)s⁢(b)s(c)s⁢s!⁢zs=1+a⁢bc⁢z+a⁢(a+1)⁢b⁢(b+1)c⁢(c+1)⁢2!⁢z2+⋯=Γ⁡(c)Γ⁡(a)⁢Γ⁡(b)⁢∑s=0∞Γ⁡(a+s)⁢Γ⁡(b+s)Γ⁡(c+s)⁢s!⁢zs,