$$U_{929}(x, y) = \frac{2 y + \sqrt{4 y^{2} + 1}}{1 - x}$$

$$Tsqrt2(n, k) = \begin{cases}\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k even, where j =} \frac{n+k} {2},\\\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k odd, where j =} \frac{n+k+1} {2},\\\end{cases} $$$$T_{929}(n, m, k) = \operatorname{Tsqrt_{2}}{\left(m,k \right)} {\binom{k + n - 1}{n}}$$