$$U_{539}(x, y) = \frac{- \sqrt{- \frac{x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{3}}{2 y^{6}} + \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{4}}{16 y^{8}}} + \frac{\left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{4 y^{4}}}{2 x}$$

$$T_{539}(n, m, k) = \begin{cases}\frac{k {\binom{k + 2 n - 1}{n}}}{k + n}&\text{if m=0} ,\ \\\frac{2 k \left(k - n\right) {\binom{k + 2 n - 1}{n}} {\binom{2 k + 2 m - 2 n - 1}{m - 1}}}{m \left(k + n\right)} \end{cases} $$