$$U_{643}(x, y) = 2 x - \sqrt{4 x^{2} + \frac{\left(\sqrt{4 y + 1} + 1\right)^{2}}{4}}$$

$$T_{643}(n, m, k) = \begin{cases}\left(-1\right)^{k}&\text{if n==0, m==0} ,\ \\\frac{\left(-1\right)^{k - 1} \cdot 4^{n} k {\binom{- \frac{k}{2} + \frac{n}{2} - 1}{n - 1}}}{2 n}&\text{if m==0, n>0} ,\ \\\frac{\left(-1\right)^{k + m + n - 1} \cdot 4^{n} k {\binom{\frac{k}{2} + \frac{n}{2} - 1}{n}} {\binom{- k + 2 m + n - 1}{m - 1}}}{m}&\text{if m>0} \end{cases} $$