$$U_{470}(x, y) = \frac{\sqrt{y \left(4 - \frac{16 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- x}}{2} \right)}}{3} \right)}}{3}\right) + 1}}{2} + \frac{1}{2}$$

$$T_{470}(n, m, k) = \begin{cases}1&\text{if m=0, n=0} ,\ \\\frac{\left(-1\right)^{m - 1} k {\binom{- k + 2 m - 1}{m - 1}}}{m}&\text{if m>0, n=0} ,\ \\\frac{\left(-1\right)^{m - 1} \left(-1\right)^{n - 1} k {\binom{- k + 2 m - 1}{m - 1}} {\binom{- m + 3 n - 1}{n - 1}}}{n} \end{cases} $$