[R] Numerical Integration in 1D

[Ravi Varadhan]

Hi max,

Prof. Ripley is right.  Your problem is that you missed a (-) sign in the
exponential.  Here is a demonstration showing the agreement between
numerical and analytical results: 

gx <- function(x, n) exp(-x) * x^n * log(x)

df <- function(n) {integrate(gx, lower=0, upper=Inf, n=n)$val}

library(numDeriv)

fx <- function(x, n) exp(-x) * x^n

gf <- function(n) {integrate(fx, lower=0, upper=Inf, n=n)$val}

> grad(x=6, func=gf)
[1] 1348.405
> 
> df(6)
[1] 1348.405
>

Ravi.


----------------------------------------------------------------------------
-------

Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology 

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan at jhmi.edu

Webpage:  http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html

 

----------------------------------------------------------------------------
--------


-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
Behalf Of Max
Sent: Friday, March 07, 2008 1:41 PM
To: r-help at stat.math.ethz.ch
Subject: [R] Numerical Integration in 1D

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?

-Max

______________________________________________
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.