\[\mathbf{J}_{n}=\begin{bmatrix}\alpha_{0}&\sqrt{\beta_{1}}&&&0\\
\sqrt{\beta_{1}}&\alpha_{1}&\sqrt{\beta_{2}}&&\\
&\ddots&\ddots&\ddots&\\
&&\sqrt{\beta_{n-2}}&\alpha_{n-2}&\sqrt{\beta_{n-1}}\\
0&&&\sqrt{\beta_{n-1}}&\alpha_{n-1}\end{bmatrix}.\]