\(D_{k,j}=\left\{\begin{matrix}-\frac{\left(N+1\right)(N-1)}{2},\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ j=k=1,\\ \frac{\tau_{k}\left(p_{N-1}^{{}^{\prime}}\left(\tau_{k}\right)+p_{N}^{{}^{\prime}}\left(\tau_{k}\right)\right)+Np_{N-1}^{{}^{\prime}}\left(\tau_{k}\right)}{\left(1-\tau_{k}^{2}\right)(p_{N-1}^{{}^{\prime}}\left(\tau_{k}\right)+p_{N}^{{}^{\prime}}\left(\tau_{k}\right))},\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2\leq j=k\leq N,\\ \frac{\left(p_{N-1}^{{}^{\prime}}\left(\tau_{k}\right)+p_{N}^{{}^{\prime}}\left(\tau_{k}\right)\right)}{\left(\tau_{k}-\tau_{j}\right)(p_{N-1}^{{}^{\prime}}\left(\tau_{k}\right)+p_{N}^{{}^{\prime}}\left(\tau_{j}\right))},\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ j\neq k.\\ \end{matrix}\right.\ \) (31)