$$U_{1188}(x, y) = \frac{\frac{2 x}{\left(1 - y\right)^{3}} + \sqrt{\frac{4 x^{2}}{\left(1 - y\right)^{6}} + 1}}{\left(1 - y\right)^{3}}$$

$$Tsqrt2(n, k) = \begin{cases}\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k even, where j =} \frac{n+k} {2},\\\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k odd, where j =} \frac{n+k+1} {2},\\\end{cases} $$$$T_{1188}(n, m, k) = k \operatorname{Tsqrt_{2}}{\left(n,k \right)} {\binom{3 k + m + 3 n - 1}{m}}$$