Geodesic
Lagrange interpolation polynomials and orthogonal Fourier--Jacobi series
Matematičeskie zametki, Tome 20 (1976) no. 2, pp. 215-226.

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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 $[a; b]\subset(-1; 1)$. 
@article{MZM_1976_20_2_a6,
     author = {A. A. Privalov},
     title = {Lagrange interpolation polynomials and orthogonal {Fourier--Jacobi} series},
     journal = {Matemati\v{c}eskie zametki},
     pages = {215--226},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_2_a6/}
}
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A. A. Privalov. Lagrange interpolation polynomials and orthogonal Fourier--Jacobi series. Matematičeskie zametki, Tome 20 (1976) no. 2, pp. 215-226. http://geodesic.mathdoc.fr/item/MZM_1976_20_2_a6/