$$U_{571}(x, y) = \frac{\sqrt{\frac{x \left(1 - \sqrt{1 - 4 y}\right)^{3}}{2 y^{3}} + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{2}}{4 y^{2}}}}{2} + \frac{1 - \sqrt{1 - 4 y}}{4 y}$$

$$T_{571}(n, m, k) = \begin{cases}\frac{\left(-1\right)^{n - 1} k \left(k + n\right) {\binom{- k + 2 n - 1}{n - 1}} {\binom{k + 2 m + n - 1}{m}}}{n \left(k + m + n\right)}&\text{if n>0} ,\ \\\frac{k {\binom{k + 2 m + n - 1}{m}}}{k + m + n}&\text{if n==0 } \end{cases} $$