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The Chebyshev polynomial $U_n(x)$ of the second kind is characterized by $$ U_n(\cos\theta)=\frac{\sin(n+1)\theta}{\sin(\theta)}. $$ It seems that $$\operatorname*{Res}_x \left( U_n(x)+tU_{n-1}(x),\...

Let us define a diagonal matrix $\mathbf{D}(\lambda) = diag(\lambda^{m_1}, \dots, \lambda^{m_n})$ with $\lambda\in\mathbb{C}$ and positive integers $m_1, \dots, m_n$. The generalized characteristic ...

Let $N_1:=\chi_{[0,1]}$ be defined as this characteristic function and $N_n:=N_{n-1}*N_1$ then this leads to polynomials with support $[0,n]$. These splines are well-studied click for wikipedia My ...