$$\begin{array}{rcll}\prod \left(n,\phi ,0\right)& =& \sqrt{\frac{1}{1-n}}{\tan }^{-1}\left(\sqrt{1-n}\tan \phi \right)& ;n<1\\ & =& \sqrt{\frac{1}{n-1}}{\tanh }^{-1}\left(\sqrt{n-1}\tan \phi \right)& ;n>1\\ & =& \tan \phi & ;n=1\end{array}$$