$$U_{321}(x, y) = \frac{\sqrt{3} \left(\sqrt{3 x y + \sin^{2}{\left(\frac{\arcsin{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}} + \sin{\left(\frac{\arcsin{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}\right)}{3 \sqrt{x}}$$

$$T_{321}(n, m, k) = \begin{cases}1&\text{if n=0 and m=0} ,\ \\\frac{k {\binom{k + 3 n - 1}{n}}}{k + 2 n}&\text{if m=0} ,\ \\\frac{\left(-1\right)^{m - 1} k {\binom{- k + 2 m - 1}{m - 1}}}{m}&\text{if m>0 and n=0} ,\ \\\frac{\left(-1\right)^{n - 1} k \left(k - 2 m\right) {\binom{k - m - 1}{m - 1}} {\binom{- k + 2 m - 2 n - 1}{n - 1}}}{m n}&\text{if m>0 and n>0} \end{cases} $$