$$U_{475}(x, y) = \frac{\left(1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- y}}{2} \right)}}{3} \right)}}{3}\right)^{2} + \sqrt{4 x \left(1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- y}}{2} \right)}}{3} \right)}}{3}\right) + \left(1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- y}}{2} \right)}}{3} \right)}}{3}\right)^{4}}}{2 - \frac{8 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- y}}{2} \right)}}{3} \right)}}{3}}$$

$$T_{475}(n, m, k) = \begin{cases}\frac{k {\binom{k - n - 1}{n - 1}}}{n}&\text{if n>0 and m=0} ,\ \\1&\text{if n=0 and m=0} ,\ \\\frac{\left(-1\right)^{m - 1} k {\binom{- k + 3 m - 1}{m - 1}}}{m}&\text{if n=0 and m>0} ,\ \\\frac{\left(-1\right)^{m - 1} k \left(k - 3 n\right) {\binom{k - n - 1}{n - 1}} {\binom{- k + 3 m + 3 n - 1}{m - 1}}}{m n}&\text{if n>0 and m>0} \end{cases} $$