$$U_{314}(x, y) = x + \frac{\sqrt{\frac{4 x}{\left(1 - y\right)^{2}} + \frac{1}{\left(1 - y\right)^{4}}}}{2} + \frac{1}{2 \left(1 - y\right)^{2}}$$

$$T_{314}(n, m, k) = \begin{cases}{\binom{2 k + m - 1}{m}}&\text{if n=0} ,\ \\\frac{2 \left(-1\right)^{n - 1} k {\binom{- 2 k + 2 n - 1}{n - 1}} {\binom{2 k + m - 2 n - 1}{m}}}{n}&\text{if n>0} \end{cases} $$