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Abstract : |
A form of Gauss-Quadrature rule over [0, 1] has been investigated that involves the derivative of the integrand at the pre-assigned left or right end node. This situation arises when the underlying polynomials are orthogonal with respect to the weight function omega(x):= 1-x over [0, 1]. Along the lines of Golub's work, the nodes and weights of the quadrature rule are computed from a Jacobi-type matrix with entries related to simple rational sequences. The structure of these sequences is based on some characteristics of the identity-type polynomials recently developed by one of the authors. The devised rule has a slight advantage over that subject to the weight function omega(x):= 1., |
