The existing LegendreGaussQuadrature class incorrectly assumes that it has converged for functions where the polynomial approximation fails in a small corner of the integral space.
This situation is handled much better with the AdaptiveQuadrature class in the path for MATH-995. This problem should be observable with any integral, but I observed it with an improper integral. The patch in MATH-995 transforms the improper integral to a proper one before applying the LegendreGaussQuadrature class (to show how it fails). It also computes the same proper integral with the Adaptive method to show the proper behavior. Cheers, Ajo.
