$$U_{408}(x, y) = - \frac{\sqrt{\frac{8 \sqrt{3} x \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 \sqrt{y}} + \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 y}}}{2} + \frac{\sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 \sqrt{y}}$$

$$T_{408}(n, m, k) = \begin{cases}- \frac{\left(-1\right)^{m + 1} k {\binom{k - n}{n}} {\binom{- k - 2 m + n - 1}{m - 1}}}{m}&\text{if m>0} ,\ \\0&\text{if n<k} ,\ \\- \frac{\left(-1\right)^{n - 1} k {\binom{- k + 2 n - 1}{n - 1}}}{n}&\text{if m=0} \end{cases} $$