Average quadrature formulas of Gauss type

In the average quadrature formulas the values of a given functionat given points are replaced by its averages over some distinctintervals. If all the intervals are of the same length, thequadrature formulas of interpolatory type and in particular,of Newton-Cotes type were constructed in Omladi (1978). Here,we construct average quadrature formulas of Gauss type for intervalsof the same length. The middle points of the intervals are zerosof polynomials, orthogonal in a technical sense.     

On Average Newton-Cotes Quadrature Formulas

In this paper we study a new type of quadrature formulas, introducedin Omladi et al. (1976). We suppose that we do not know thevalues of the function at given points, but its averages oversome distinct intervals. If all of the intervals are of thesame length, we can construct the interpolatory type quadratureformulas. We give also the generalizations of the Newton-Cotesformulas.