ANZIAM  J.  48 (2007), 567-581
Monotonicity of the error term in Gauss–Turán quadratures for analytic functions

Gradimir V. Milovanović
  Department of Mathematics
  University of Niš
  P. O. Box 73
  18000 Niš
  Serbia
    grade@ni.ac.yu
Miodrag M. Spalević
  Department of Mathematics and Informatics
  University of Kragujevac
  P. O. Box 60
  34000 Kragujevac
  Serbia
    spale@kg.ac.yu


Abstract
For Gauss–Turán quadrature formulae with an even weight function on the interval [-1,1] and functions analytic in regions of the complex plane which contain in their interiors a circle of radius greater than 1, the error term is investigated. In some particular cases we prove that the error decreases monotonically to zero. Also, for certain more general cases, we illustrate how to check numerically if this property holds. Some l^2-error estimates are considered.
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