Chebyshev-Markov cosine fractions in the approximate integration and solution of integral equations (Q745270)

The authors use a quadrature formula of Gauss type to approximate solving the Fredholm integral equation of the second kind \[ y(s) - \lambda \int_{-1}^{1}\frac{h(s,t)y(t)dt}{\sqrt{1-t^{2}}}= f(s) \] with a special kernel and \( f(s)\in C[-1,1]\). The quadrature formula is constructed using the weighted system of the orthogonal rational functions (named cosine fractions). Numerical examples and the comparison of this method with the quadrature formula of Chebyshev are not given.