$$U_{433}(x, y) = \frac{\sqrt{4 y + 1} + 1}{2 \left(1 - x\right)^{2}}$$

$$T_{433}(n, m, k) = \begin{cases}1&\text{if n=0 and m=0 } ,\ \\{\binom{2 k + n - 1}{n}}&\text{if m=0 and n>0} ,\ \\\frac{\left(-1\right)^{m - 1} k {\binom{- k + 2 m - 1}{m - 1}} {\binom{2 k + n - 1}{n}}}{m} \end{cases} $$