$$U_{909}(x, y) = - x - \frac{y}{2} + \frac{\sqrt{4 x^{2} - 4 x + y^{2} + y \left(- 4 x - 2\right) + 1}}{2} + \frac{1}{2}$$

$$T_{909}(n, m, k) = \begin{cases}- \frac{2^{n} k {\binom{- k + m + n}{m}} {\binom{- k + m + n - 1}{n - 1}}}{n}&\text{if n>0} ,\ \\1&\text{if n==0, m==0} ,\ \\\left(-1\right)^{m} {\binom{k}{m}}&\text{if n==0} \end{cases} $$