$$U_{585}(x, y) = \frac{\sqrt{3} \left(2 - \frac{8 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- x}}{2} \right)}}{3} \right)}}{3}\right) \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 \sqrt{y}}$$

$$T_{585}(n, m, k) = \begin{cases}\frac{k {\binom{k + 3 m - 1}{m}}}{k + 2 m}&\text{if n==0} ,\ \\\frac{\left(-1\right)^{n - 1} k^{2} {\binom{- k + 3 n - 1}{n - 1}} {\binom{k + 3 m - 1}{m}}}{n \left(k + 2 m\right)}&\text{if n>0} \end{cases} $$