$$U_{570}(x, y) = \frac{\left(1 - \sqrt{1 - 4 y}\right) \left(1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- x}}{2} \right)}}{3} \right)}}{3}\right)}{2 y}$$

$$T_{570}(n, m, k) = \begin{cases}\frac{k {\binom{k + 2 m - 1}{m}}}{k + m}&\text{if n==0} ,\ \\\frac{\left(-1\right)^{n - 1} k^{2} {\binom{- k + 3 n - 1}{n - 1}} {\binom{k + 2 m - 1}{m}}}{n \left(k + m\right)}&\text{if n>0} \end{cases} $$