A solution of Problem 33 of P. Turán's (Q1340024)

The Problem 33 of \textit{P. Turán} [J. Approximation Theory 29, 23-89 (1980; Zbl 0454.41001)] concerns with the regularity of the problem of Hermite-Birkhoff \((0,2)\)-interpolation on a triangular matrix of nodes. In this paper the author has given a solution of the problem involving the zeros of Jacobi's polynomials. A partial answer to the problem involving Legendre polynomials is reported to have also been worked out by the author earlier.