$$U_{694}(x, y) = \frac{1 - \sqrt{4 x \left(1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- y}}{2} \right)}}{3} \right)}}{3}\right) + 1}}{2 x}$$

$$T_{694}(n, m, k) = \begin{cases}\frac{\left(-1\right)^{- k + n} k {\binom{k + 2 n - 1}{k + n - 1}}}{k + n}&\text{if m=0} ,\ \\\frac{\left(-1\right)^{- k + n} \left(-1\right)^{m - 1} k {\binom{k + 2 n - 1}{k + n - 1}} {\binom{- k + 3 m - n - 1}{m - 1}}}{m}&\text{if m>0} \end{cases} $$