A recursive algorithm by the moments method to evaluate a class of numerical integrals over an infinite interval (Q1895987)

For computing integrals over an infinite interval a three-terms recursive formula with coefficients evaluated by the moments method is obtained. The following functional \(c(f) = \int^{+\infty}_0 f(x) w(x) e^{- \alpha x} dx\), \(w(x) > 0\) over \((0, +\infty)\), is studied, and it is supposed that the function space, on which the functional is defined, contains the polynomial case. The integral is fully determined by the moments \(C_i = c(\varphi_i) = \int^{+\infty}_0 \varphi_i (x) w(x) e^{-\alpha x} dx\), \(\varphi_i(x) = x^i\), \(i = 0,1, \dots\) .