(untitled) (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.