Lagrange interpolation polynomials and orthogonal Fourier–Jacobi series

Let $\alpha>-1$ and $\beta>-1$. Then a function $f(x)$, continuous on the segment $[-1; 1]$, exists such that the sequence of Lagrange interpolation polynomials constructed from the roots of Jacobi polynomials diverges almost everywhere on $[-1; 1]$, and, at the same time, the Fourier–Jacobi series of function $f(x)$ converges uniformly to $f(x)$ on any segment $[a; b]\subset(-1; 1)$.