From: Max <mnevill_at_exitcheck.net>

Date: Fri, 07 Mar 2008 11:14:21 -0800

R-help_at_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. Received on Fri 07 Mar 2008 - 19:13:37 GMT

Date: Fri, 07 Mar 2008 11:14:21 -0800

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.

> 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_at_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. Received on Fri 07 Mar 2008 - 19:13:37 GMT

Archive maintained by Robert King, hosted by
the discipline of
statistics at the
University of Newcastle,
Australia.

Archive generated by hypermail 2.2.0, at Fri 07 Mar 2008 - 21:30:19 GMT.

*
Mailing list information is available at https://stat.ethz.ch/mailman/listinfo/r-help.
Please read the posting
guide before posting to the list.
*