A NOTE ON THE CONTOUR INTEGRAL-REPRESENTATION OF THE REMAINDER TERM FOR A GAUSS-CHEBYSHEV QUADRATURE RULE

It is shown that the kernel Kn(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, assumes its largest modulus on the imaginary axis if ρ ≥ ρn+1, where ρn+1 is the root of a certain algebraic equations. If 1 < ρ < ρn+1, the maximum is attained near the imaginary axis within an angular distance less than π/(2n+2). The bounds {ρn+1} decrease monotonically to 1.