$$U_{622}(x, y) = \frac{\left(1 - \frac{4 \sin^{2}{\left(\frac{\arcsin{\left(\frac{3 \sqrt{3} \sqrt{- y}}{2} \right)}}{3} \right)}}{3}\right) \left(- 2 x - \sqrt{1 - 4 x} + 1\right)}{2 x^{2}}$$

$$T_{622}(n, m, k) = \begin{cases}\frac{k {\binom{2 k + 2 n}{n}}}{k + n}&\text{if m=0 } ,\ \\\frac{\left(-1\right)^{m - 1} k^{2} {\binom{2 k + 2 n}{n}} {\binom{- k + 3 m - 1}{m - 1}}}{m \left(k + n\right)}&\text{if m>0} \end{cases} $$