$$U_{590}(x, y) = \frac{\left(1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- x}}{2} \right)}}{3} \right)}}{3}\right) \left(\sqrt{4 y + 1} + 1\right)}{2}$$

$$T_{590}(n, m, k) = \begin{cases}1&\text{if n=0,m=0} ,\ \\\frac{\left(-1\right)^{n - 1} k {\binom{- k + 3 n - 1}{n - 1}}}{n}&\text{if m=0} ,\ \\\frac{\left(-1\right)^{m - 1} \left(-1\right)^{n - 1} k^{2} {\binom{- k + 2 m - 1}{m - 1}} {\binom{- k + 3 n - 1}{n - 1}}}{m n}&\text{if n>0, m>0} ,\ \\\frac{\left(-1\right)^{m - 1} k {\binom{- k + 2 m - 1}{m - 1}}}{m}&\text{if n=0} \end{cases} $$