$$U_{100}(x, y) = \frac{1}{\sqrt{- 4 y^{2} + \left(x - 1\right)^{2}}}$$

$$T_{100}(n, m, k) = 2^{m - 1} \left(\left(-1\right)^{m} + 1\right) {\binom{\frac{k}{2} + \frac{m}{2} - 1}{\frac{m}{2}}} {\binom{k + m + n - 1}{n}}$$