Laguerre is defined only in [0,+ve Inf] Hermite is defined in [-Inf,+Inf] I have two issues with the above: 1: Cant imagine how someone would use AQ. Which means as Gilles noticed, you can't focus on the hard to converge sections of the integral. 2: If you use the integration without AQ. Any function that has a high frequency region somewhere off the region where the polynomial focuses, the integral probably won't converge. For Hermite with its weighting in e^(-x^2) ... good luck with convergence with say computing CDF of N(0,100) or for that matter N(100,1). For an idea look at : https://en.wikipedia.org/wiki/Gauss%E2%80%93Hermite_quadrature
I think by now Gilles might have finished his attempt at Gauss-Hermite ... perhaps he can say what he saw on tests. That was easier to answer! Cheers, Ajo On Sat, Jul 20, 2013 at 11:11 AM, Ted Dunning <ted.dunn...@gmail.com> wrote: > The math is quite simple. > > What is not clear is what the numerical properties are for substitution of > the sort being advocated. > > Which functions will do better with substitution? Which will do better > with Laguerre polynomials? > > > > On Sat, Jul 20, 2013 at 8:59 AM, Ajo Fod <ajo....@gmail.com> wrote: > > > The method is described here: > > http://en.wikipedia.org/wiki/Integration_by_substitution > > > > My patch uses it for improper integration via the change of variable > > t/(1-t^2) as suggested in : > > http://en.wikipedia.org/wiki/Numerical_integration > > > > Please reach back if anyone understands this concept. > > > > Cheers, > > -Ajo > > >
