12⁢π⁢∫-∞∞Γ⁡(a+ⅈ⁢t)⁢Γ⁡(b+ⅈ⁢t)⁢Γ⁡(c-ⅈ⁢t)⁢Γ⁡(d-ⅈ⁢t)⁢ⅆ⁡t=Γ⁡(a+c)⁢Γ⁡(a+d)⁢Γ⁡(b+c)⁢Γ⁡(b+d)Γ⁡(a+b+c+d),