Re: [R] Numerical Integration in 1D

From: Prof Brian Ripley <ripley_at_stats.ox.ac.uk>
Date: Fri, 07 Mar 2008 18:51:15 +0000 (GMT)

> 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

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