$$U_{522}(x, y) = \frac{- \sqrt{- \frac{4 x}{\left(1 - y\right)^{3}} + \frac{1}{\left(1 - y\right)^{4}}} + \frac{1}{\left(1 - y\right)^{2}}}{2 x}$$

$$T_{522}(n, m, k) = \frac{k {\binom{k + 2 n - 1}{n}} {\binom{k + m - n - 1}{m}}}{k + n}$$