$$U_{584}(x, y) = \frac{\left(1 - 4 y\right)^{\frac{3}{2}} \left(1 - \sqrt{- \frac{4 x}{\left(1 - 4 y\right)^{2}} + 1}\right)}{2 x}$$

$$T_{584}(n, m, k) = \frac{4^{m} k {\binom{k + 2 n - 1}{n}} {\binom{\frac{k}{2} + m + 2 n - 1}{m}}}{k + n}$$