Inverse Hyperbolic Function - Addition Formulae

Addition Formulae


\begin{align}\operatorname{arsinh} \;u + \operatorname{arcosh} \;v & = \operatorname{arsinh} \left(u v + \sqrt{(1 + u^2) (v^2 - 1)}\right) \\ & = \operatorname{arcosh} \left(v \sqrt{1 + u^2} + u \sqrt{v^2 - 1}\right) \end{align}

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