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On the remainder of Gaussian quadrature formulas for Bernstein-Szegő weight functions. (English) Zbl 0796.41025
Summary: We give an explicit expression for the kernel of the error functional for Gaussian quadrature formulas with respect to weight functions of Bernstein-Szegő type, i.e., weight functions of the form $$(1-x)^ \alpha (1+x)^ \beta/ \rho(x)$$, $$x\in (-1,1)$$, where $$\alpha,\beta\in \{-{1\over 2}, {1\over 2}\}$$ and $$\rho$$ 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.

##### MSC:
 41A55 Approximate quadratures 33C65 Appell, Horn and Lauricella functions