# [R] logarithmic integrals in R?

Hans W. Borchers hwborchers at googlemail.com
Sun May 30 08:33:31 CEST 2010

Oliver Kullmann <O.Kullmann <at> swansea.ac.uk> writes:
>
> Thanks for the information.

What I meant were formulas like

\int 1/\log(t)^2 dt = -t/\log(t) + li(t)

\int 1/\log(t)^3 dt = 1/2 * ( -t/\log(t)^2 - t/\log(t) + li(t) )

and higher forms that can be expressed through the Gamma function.
I am certain I 've seen them in AandS' handbook (where else?), but
sure cannot remember in which chapter or page.

Which logarithmic integrals do you really need, and on what range?

Regards,
Hans Werner

> 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 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.
>
[...]
>
> 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
>