Journal of computational and applied mathematics vol:50 issue:1-3 pages:145-158
Gregory-type formulae associated with the class of composite Newton-Cotes quadrature rules of the closed type are established. Furthermore, it is shown how these formulae can be extended by introducing mixed interpolation functions which contain a polynomial and a trigonometric part. The case of the modified Gregory rules associated with the composite Simpson quadrature rule is worked out in detail. Also the error term is analysed and the obtained rules are numerically tested.