[R] logarithmic integrals in R?

[Oliver Kullmann]

Thanks for the information.

On Sat, May 29, 2010 at 01:15:29PM +0000, Hans W. Borchers wrote:
> Oliver Kullmann <O.Kullmann <at> swansea.ac.uk> writes:
> 
> > 
> > Hello,
> > 
> > I couldn't find information on whether the logarithmic integrals
> > 
> > Li_m(x) = integral_0^x log(t)^(-m) dt
> > 
> > for x >= 0 are available in R?
> 
> I saw your request only this weekend.
> The first logarithmic integral can be computed using the exponential
> integral Ei(x) per
> 
>     li(x) = Ei(log(x))
>

I found gsl at http://cran.r-project.org/web/packages/gsl/index.html.
 
> and elliptic integrals are part of the 'gsl' package, so
> 
>     library('gsl')
>     x <- seq(2, 10, by=0.5)
>     y <- expint_Ei(log(x))
>     y
> 
> See e.g. the Handbook of Mathematical Functions for how to reduce higher
> logarithmic integrals.

However here I wasn't succesful: Going through the chapter

http://www.math.ucla.edu/~cbm/aands/page_228.htm

I didn't find any mentioning of the higher logarithmic integrals.

> Another possibility is to use the Web API of 'keisan', the calculation
> library of Casio.
> 

Interesting; but again only li(x).

Also a google search on "higher logarithmic integrals", "logarithmic integrals"
or "li_n(x)" doesn't reveal anything, so I would be thankful for a hint.

Thanks again!

Oliver