2.10.4 面积函数的和与差

$$\begin{array}{}\text{(2.219)}& \mathrm{Arsinh}x\pm \mathrm{Arsinh}y=\mathrm{Arsinh}\left(x\sqrt{1+y^2}\pm y\sqrt{1+x^2}\right),\end{array}$$$$\begin{array}{}\text{(2.220)}& \mathrm{Arcosh}x\pm \mathrm{Arcosh}y=\mathrm{Arcosh}\left(xy\pm \sqrt{\left(x^2-1\right)\left(y^2-1\right)}\right),\end{array}$$$$\begin{array}{}\text{(2.221)}& \mathrm{Artanh}x\pm \mathrm{Artanh}y=\mathrm{Artanh}\frac{x\pm y}{1\pm xy}.\end{array}$$