It is shown that there do not exist integration rules of the form $\int^\infty_0 f(x) dx = \sum_{i=1}^n w_if(x_i) + C_nf^{(m)}(\xi),\quad 0 < \xi < \infty$. Journal ...

It is shown that the Kronrod extension to the $n$-point Gauss integration rule, with respect to the weight function $(1 - x^2)^{\mu-1/2}, 0 < \mu \leqslant 2, \mu ...