$$U_{631}(x, y) = 2 x - \sqrt{4 x^{2} + \frac{1}{\left(1 - y\right)^{4}}}$$

$$T_{631}(n, m, k) = \begin{cases}\left(-1\right)^{k} {\binom{2 k + m - 1}{m}}&\text{if n==0} ,\ \\\frac{\left(-1\right)^{k + 1} \cdot 4^{n} k {\binom{- \frac{k}{2} + \frac{n}{2} - 1}{n - 1}} {\binom{2 k + m - 2 n - 1}{m}}}{2 n}&\text{if n>0} \end{cases} $$