$$U_{931}(x, y) = \frac{\sqrt{- 8 x y - 4 x \sqrt{4 y^{2} + 1} + 1}}{2} + \frac{1}{2}$$

$$Tsqrt2(n, k) = \begin{cases}\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k even, where j =} \frac{n+k} {2},\\\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k odd, where j =} \frac{n+k+1} {2},\\\end{cases} $$$$T_{931}(n, m, k) = \begin{cases}1&\text{if n = 0,m = 0} ,\ \\0&\text{if n = 0,m > 0} ,\ \\- \frac{k \operatorname{Tsqrt_{2}}{\left(m,n \right)} {\binom{- k + 2 n - 1}{n - 1}}}{n} \end{cases} $$