The numerical computation of some integrals on the real line (Q1971844)

The purpose of this paper is to present certain results concerning the approximation of integrals of type \[ I(f, t)= \int_{\mathbb{R}} f(x)K(x, t) e^{-x^2}|x|^\alpha dx,\quad \alpha>-1, \] where \(|x-t|^\lambda\), \(-1<\lambda< 0\) is the weakly singular algebraic kernel, for ``large'' values of the parameter \(t\). The numerical results obtained by using the generalized Gauss-Hermite rules are given. Moreover, the authors consider strongly oscillatory kernels of type \[ K_1(x, t)= \sin(tx^2),\quad K_2(x, t)= \cos(tx^2). \]