$$U_{423}(x, y) = \sqrt[3]{\frac{x}{2} + \frac{\sqrt{3} \sqrt{x \left(27 x + \frac{4}{\left(1 - 4 y\right)^{\frac{3}{2}}}\right)}}{18} + \frac{1}{27 \left(1 - 4 y\right)^{\frac{3}{2}}}} + \frac{1}{\left(9 - 36 y\right) \sqrt[3]{\frac{x}{2} + \frac{\sqrt{3} \sqrt{x \left(27 x + \frac{4}{\left(1 - 4 y\right)^{\frac{3}{2}}}\right)}}{18} + \frac{1}{27 \left(1 - 4 y\right)^{\frac{3}{2}}}}} + \frac{1}{3 \sqrt{1 - 4 y}}$$

$$T_{423}(n, m, k) = \begin{cases}1&\text{if m=0,n=0} ,\ \\\frac{\left(-1\right)^{m - 1} \cdot 4^{m} {\binom{- \frac{k}{2} + \frac{n}{2} - 1}{m - 1}}}{2 m}&\text{if n=0} ,\ \\\frac{4^{m} k {\binom{k - 2 n - 1}{n - 1}} {\binom{\frac{k}{2} + m - \frac{3 n}{2} - 1}{m}}}{n}&\text{if n>0} \end{cases} $$