On a conjectured inequality for the largest zero of Jacobi polynomials

P. Leopardi and the author recently investigated, among other things, the validity of the inequality between the largest zero and of the Jacobi polynomial resp. alpha > 1, beta > 1. The domain in the parameter space (alpha, beta) in which the inequality holds for all n >= 1, conjectured by us, is shown here to require a small adjustment-the deletion of a very narrow lens-shaped region in the square {1 <alpha < 1/2, 1/2 <beta < 0}.