The remainder term for analytic functions of Gauss-Lobatto quadratures (Q5961654)

In this paper the author studies and solves some conjectures of \textit{W. Gautschi} [Rocky Mt. J. Math. 21, No. 1, 209-226 (1991; Zbl 0749.41026)] on location of the maximum point for some kernels associated with the representation of the remainder term of Gauss-Lobatto quadrature rules. The author believes that the techniques of the paper may as well provide an analytic proof for some conjectures of Gautschi on Gauss-Radau quadratures, though the calculations may be more complicated. Some extensions to Gaussian quadrature rules are given. The author also gives a couple of numerical examples which show the sharpness attained using the results of the paper in the estimation of errors.