$$U_{634}(x, y) = 2 x - \sqrt{4 x^{2} + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{2}}{4 y^{2}}}$$

$$T_{634}(n, m, k) = \begin{cases}\left(-1\right)^{k}&\text{if m=0,n=0} ,\ \\\frac{\left(-1\right)^{- k + n} \left(-1\right)^{m - 1} \cdot 4^{n} k {\binom{\frac{k}{2} + \frac{n}{2} - 1}{n}} {\binom{- k - m + n - 1}{m - 1}}}{m}&\text{if m > 0} ,\ \\\frac{\left(-1\right)^{k - 1} \cdot 4^{n} k {\binom{- \frac{k}{2} + \frac{n}{2} - 1}{n - 1}}}{2 n} \end{cases} $$