RESUMEN

It is shown that the kernel K_n (z), n (even) ≥ 2, in the contour integral representation of the remainder term of the n-point Gauss formula for the Chebyshev weight function of the second kind, as z varies on the ellipse E_ρ = {z:z = ρ e ^iv + ρ^-1 e ^-iv , 0 ≤ v ≤ 2 π}, ρ – 1, assumes its largest modulus on the imaginary axis if ρ  ≥  ρ _{n + 1}, where ρ _{n + 1} is the root of a certain algebraic equation. If 1 < ρ < ρ _{n + 1}, the maximum is attained near the imaginary axis within an angular distance less than π / (2n + 2). The bounds { ρ _{n + 1}} decrease monotonically to 1.