$$U_{588}(x, y) = - \frac{2 \sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 \sqrt{y} \left(\frac{8 \sqrt{3} x \sin^{3}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{9 y^{\frac{3}{2}}} - 1\right)}$$

$$T_{588}(n, m, k) = \frac{\left(k + 3 n\right) {\binom{k + n - 1}{n}} {\binom{k + 3 m + 3 n - 1}{m}}}{k + 2 m + 3 n}$$