$$U_{922}(x, y) = \frac{y}{2} + \frac{\sqrt{\frac{4 x + y - 1}{y - 1}} \left(y - 1\right)}{2} - \frac{1}{2}$$

$$T_{922}(n, m, k) = \begin{cases}\left(-1\right)^{k + m} {\binom{k}{m}}&\text{if n = 0} ,\ \\\frac{\left(-1\right)^{k - 1} k {\binom{- k + 2 n - 1}{n - 1}} {\binom{- k + m + n - 1}{m}}}{n}&\text{if n > 0} \end{cases} $$