$$U_{586}(x, y) = \frac{\sqrt{\frac{32 \sqrt{3} x \sin^{3}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{9 y^{\frac{3}{2}}} + \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 y}}}{2} + \frac{\sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 \sqrt{y}}$$

$$T_{586}(n, m, k) = \begin{cases}\frac{k {\binom{k + 3 m + n - 1}{m}}}{k + 2 m + n}&\text{if n==0} ,\ \\\frac{\left(-1\right)^{n - 1} k \left(k + n\right) {\binom{- k + 2 n - 1}{n - 1}} {\binom{k + 3 m + n - 1}{m}}}{n \left(k + 2 m + n\right)}&\text{if n>0} \end{cases} $$