$$U_{594}(x, y) = \frac{4 - 4 \sqrt{- \frac{x \left(\sqrt{4 y + 1} + 1\right)^{4}}{4} + 1}}{x \left(\sqrt{4 y + 1} + 1\right)^{3}}$$

$$T_{594}(n, m, k) = \begin{cases}\frac{k {\binom{k + 2 n - 1}{n}}}{k + n}&\text{if m==0} ,\ \\\frac{\left(-1\right)^{m - 1} k \left(k + 4 n\right) {\binom{k + 2 n - 1}{n}} {\binom{- k + 2 m - 4 n - 1}{m - 1}}}{m \left(k + n\right)}&\text{if m>0} \end{cases} $$