Numerical Integration in 1D
On Fri, 7 Mar 2008, Max wrote:
Dear UseRs, I'm curious about the derivative of n!. We know that Gamma(n+1)=n! So when on takes the derivative of Gamma(n+1) we get Int(ln(x)*exp(-x)*x^n,x=0..Inf). I've tried code like
integrand<-function(x) {log(x)*exp(x)*x^n}
integrate(integrand,lower=0,upper=Inf)
It seems that R doesn't like to integrate for any n, and I was wondering if anyone knew a way around this?
ln(x) e^x x^n is not integrable on (0, Inf). You presumably slipped over a minus sign, but your definition of gamma(n) is wrong -- see ?gamma. integrate(function(x) exp(-x)*x^n, lower=0, upper=Inf) will work for gamma(n+1).
Brian D. Ripley, ripley at stats.ox.ac.uk Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UK Fax: +44 1865 272595