F⁡(a,ba-b+1;z)=(1-z)-a⁢Γ⁡(a-b+1)⁢Γ⁡(12)Γ⁡(12⁢a+12)⁢Γ⁡(12⁢a-b+1)⁢F⁡(12⁢a,12⁢a-b+1212;(z+1z-1)2)+(1+z)⁢(1-z)-a-1⁢Γ⁡(a-b+1)⁢Γ⁡(-12)Γ⁡(12⁢a)⁢Γ⁡(12⁢a-b+12)⁢F⁡(12⁢a+12,12⁢a-b+132;(z+1z-1)2),