The authors propose replacing the classical Gauss-Laguerre quadrature formula over an infinite interval, by a truncated version of it, obtained by eliminating the last part of its nodes. An error estimate for this new quadrature is obtained, which includes, as a particular case, the estimate for the error term of the given Gauss-Laguerre quadrature. A similar new error bounds are obtained for corresponding product-type rules, having a kernel with singularities.
The last section is dedicated to define, using the truncated product rules constructed before, Nyström-type interpolants for a class of integral equations whose solution decay exponentially to a constant, at infinity, and to prove the stability and the convergence estimates for them. Numerical experiments are performed using Matlab, for a nontruncated product rule and for three particular truncated rules, obtaining an accuracy similar to that given by the complete rule.