Geodesic
A~Criterion for the Uniform Convergence of the Lagrange--Jacobi Interpolation Process
Matematičeskie zametki, Tome 79 (2006) no. 2, pp. 254-266.

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We obtain a uniform and sufficient condition for the convergence of the Lagrange interpolation process with Jacobi nodes on a closed interval $[a,b]\subset(-1,1)$. The condition is stated in terms of the second differences of the interpolated function and uses its values only at the interpolation nodes. Some well-known criteria for uniform convergence are obtained as a consequence of our result. 
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V. V. Novikov. A~Criterion for the Uniform Convergence of the Lagrange--Jacobi Interpolation Process. Matematičeskie zametki, Tome 79 (2006) no. 2, pp. 254-266. http://geodesic.mathdoc.fr/item/MZM_2006_79_2_a8/

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