For \(q,\lambda \in \mathbb {R}\), set \(u=\log ((1-\lambda )/\lambda )\) and define \(\rho (q,\lambda )=\sqrt{\sinh (u/q)/\sinh (u/(q/(q-1)))}\), where division by zero is zero, \(\log 0=0\), \(\log x=\log |x|\) for \(x\lt 0\), and \(\sqrt x=0\) for \(x\le 0\).

For \(\lambda \in \mathbb {R}\), define \(C(\lambda )=e\) if \(\lambda =1/2\), and \(C(\lambda )=((1-\lambda )/\lambda )^{1/(2(1-2\lambda ))}\) otherwise, where division by zero is zero; for \(x\lt 0\), \(x^r=|x|^r\cos (\pi r)\); and \(0^r=0\) for \(r\ne 0\), while \(0^0=1\).