On the Remainder of Gaussian Quadrature Formulas for Bernstein-szegö Weight Functions
نویسنده
چکیده
We give an explicit expression for the kernel of the error functional for Gaussian quadrature formulas with respect to weight functions of BernsteinSzegö type, i.e., weight functions of the form (1 x)"(l + x)ß /p(x), x e (-1, 1), where a, ß £ {-\,\} and p is a polynomial of arbitrary degree which is positive on [-1, 1]. With the help of this result the norm of the error functional can easily be calculated explicitly for a wide subclass of these weight functions.
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