A Criterion for the Uniform Convergence of the Lagrange-Jacobi Interpolation Process.

We obtain a uniform and sufficient condition for the convergence of the Lagrange interpolation process with Jacobi nodes on a closed interval [ a, b] ⊂ (−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. [ABSTRACT FROM AUTHOR]