]> $$\begin{array}{rcccl}\text{legendre\_q}\left(\mathrm{0,}x\right)& =& Q_0\left(x\right)& =& \frac{1}{2}\ln \left(\frac{1+x}{1-x}\right)\\ \text{legendre\_q}\left(\mathrm{1,}x\right)& =& Q_1\left(x\right)& =& \frac{x}{2}\ln \left(\frac{1+x}{1-x}\right)-1\end{array}$$