Lobatto and Radau positive quadrature formulas for linear combinations of Jacobi polynomials
For a given $θ\in (-1,1)$, we find out all parameters $α,β\in \{0,1\}$ such that, there exists a linear combination of Jacobi polynomials $J_{n+1}^{(α,β)}(x)-C J_{n}^{(α,β)}(x)$ which generates a Lobatto (Radau) positive quadrature formula of degree of exactness \textcolor{red}{$2n+2$ ($2n+1$)} and contains the point $θ$ as a node. These positive quadratures are very useful in studying problems in one-sided polynomial $L_1$ approximation.
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