Summability of Jacobi Series

The positivity of some Cesàro mean is proven for Jacobi series Σ aₙPₙ(α ,β )(x),α ,β - 1/2. This has applications to the mean convergence of Lagrange interpolation at the zeros of Jacobi polynomials. The positivity of the (C,α + β + 2) means is conjectured and proven for some (α ,β ). One consequence of this conjecture would be the complete monotonicity of x- c(x² + 1)- c,c 1.