$$U_{639}(x, y) = 2 x + \sqrt{4 x^{2} + \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 y}}$$

$$T_{639}(n, m, k) = \begin{cases}1&\text{if m = 0,n = 0} ,\ \\\frac{\left(-1\right)^{m - 1} \cdot 4^{n} k {\binom{\frac{k}{2} + \frac{n}{2} - 1}{n}} {\binom{- k - 2 m + n - 1}{m - 1}}}{m}&\text{if m > 0} ,\ \\\frac{\left(-1\right)^{n - 1} \cdot 4^{n} k {\binom{- \frac{k}{2} + \frac{n}{2} - 1}{n - 1}}}{2 n} \end{cases} $$