Prof Brian Ripley formulated on Friday : > 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).
I did miss a minus sign in the integration, which explains part of my problems. The function of interest is the derivative of Gamma(n+1) with respect to n, but obviously integrated over x from 0 to Infinity. What happens now is: > integrand<-function(x) {log(x)*exp(-x)*x^n} > integrate(integrand,lower=0,upper=Inf) Error in f(x, ...) : object "n" not found Any ideas on how to get around this error? ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.