$$U_{589}(x, y) = \frac{3 \sqrt{3} y^{\frac{3}{2}} \left(1 - \sqrt{- \frac{64 x \sin^{4}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{9 y^{2}} + 1}\right)}{16 x \sin^{3}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}$$

$$T_{589}(n, m, k) = \frac{k \left(k + 4 n\right) {\binom{k + 2 n - 1}{n}} {\binom{k + 3 m + 4 n - 1}{m}}}{\left(k + n\right) \left(k + 2 m + 4 n\right)}$$