ABSTRACT
The interpolatory quadrature rules are based on the notion that the nodes (quadrature points) must be preassigned equidistantly or with some other kind of fixed distribution. As mentioned in Kowalewski (1932), Gauss was the first to realize that a suitable variation of the nodes leads to better accuracy in general, and this fundamental result of Gauss started many variations and generalizations of the Gaussian formulas of the type Iba(f) =
∑n k=0 wk f (xk), where the weights wk are positive zeros of certain
orthogonal polynomials and the nodes xk are distinct points in the interval (−1, 1). We will study some extended Gaussian rules and provide tables of their nodes and weights. Gaussian moments are discussed in detail and presented in a tabular form. The optimal Gaussian rule of the highest degree of precision is presented.
