Singularity and Quadrature Regularity of $(0,1,…,m-2,m)$-Interpolation on the Zeros of Jacobi Polynomials (Journal of Computational Mathematics, 2021)
In this paper we show that, if a problem of $(0,1,…,m-2,m)$-interpolation on the zeros of the Jacobi polynomials $P^{α,β}_n(x) (α,β≥ -1)$ has infinite solutions, then the general form of the solutions is $f_0(x)+Cf(x)$ with an arbitrary constant $C$, where $f_0(x)$ and $f(x)$ are fixed polynomials of degree $≤ mn-1$. Moreover, the explicit form of $f(x)$ is given. A necessary and sufficient condition of quadrature regularity of the interpolation in a manageable form is also established.