Strong asymptotics in Lagrange interpolation with equidistant nodes

In this paper we prove three conjectures of Revers on Lagrange interpolation for f_λ(t)=|t|^λ,λ>0, at equidistant nodes. In particular, we describe the rate of divergence of the Lagrange interpolants L_N( f_λ,t) for 0<|t|<1, and discuss their convergence at t=0. We also establish an asymptotic relation for max_|t|1| |t|^λ−L_N( f_λ,t)|. The proofs are based on strong asymptotics for |t|^λ−L_N( f_λ,t), 0|t|<1.