Error bounds for Gauss-Kronrod quadrature formulae

We consider the Gauss-Kronrod quadrature formulae for the Bernstein-Szegoź weight functions consisting of any one of the four Chebyshev weights divided by the polynomial ź(t)=1ź4ź(1+ź)2t2,tź(ź1,1),ź1<ź≤0$\rho (t)=1-\frac {4\gamma }{(1+\gamma )^{2}}\,t^{...

The aim of this paper is to derive quadrature formulae of Gauss type based on Euler identities. First, we derive quadrature formulae where the integral over [0,1] is approximated by values of the function in three points: x,1/2 and 1-x. As special cases,...

With the help of a new representation of the Stieltjes polynomial it is shown by using Bessel functions that the Stieltjes polynomial with respect to the ultraspherical weight function with parameter $\lambda$ has only few real zeros for $\lambda > 3$ ...