$$U_{763}(x, y) = \frac{\left(1 - \sqrt{- 4 x \sqrt{4 y + 1} + 1}\right)^{3}}{8 x^{3} \left(4 y + 1\right)}$$

$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{763}(n, m, k) = \frac{3 k \operatorname{Tsqrt}{\left(m,k + n \right)} {\binom{3 k + 2 n}{n}}}{3 k + 2 n}$$