Remark on algorithm 107: Gauss's method

Recently, Gautschi introduced so-called generalized Gauss-Radau and Gauss-Lobatto formulae which are quadrature formulae of Gaussian type involving not only the values but also the derivatives of the function at the endpoints. In the present note we ...

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,...

First we derive asymptotics for the derivatives of $s$-orthogonal polynomials and the derivatives of Cauchy principal value integrals associated with $s$-orthogonal polynomials. With the help of these results asymptotics for the quadrature weights of ...