Re: [Help-gsl] definition of dilogarithm in GSL

[Brian Gough]

At Mon, 01 Oct 2007 21:27:32 +0200,
Paul Zimmermann wrote:
> we are about the implement a dilogarithm function in MPFR. Looking at the
> different definitions, it seems the GSL definition is not the "standard"
> one in the Abramowitz&Stegun sense, but more what is commonly designed as
> Li2(x) [as the GSL manual admits it].
> 
> This is quite annoying, since if we introduce a function mpfr_dilog in
> MPFR, it will be either inconsistent with A&S, or inconsistent with GSL,
> and in both cases will probably confuse the users.
> 
> One solution would be for us to only export a function mpfr_li2, which would
> correspond to the "common" definition of Li2(x), and to the gsl_sf_dilog
> function.
> 
> Would that be ok for you? Can you explain why you choosed that mathematical
> definition for gsl_sf_dilog, or that name instead of gsl_sf_li2?

Hello,

Thanks for your email.  If you want an unambiguous name then using
mpfr_li2 would probably be the best choice.

I believe the reason that GSL uses the name gsl_sf_dilog is that the
dilogarithm is most commonly (correctly?) defined as Li2, and A&S is
in the minority calling the Spence integral a dilogarithm.

I've cc'ed this email to Gerard Jungman the original author of the GSL
dilogarithm function for any further comments.

-- 
Brian Gough

GNU Scientific Library -
http://www.gnu.org/software/gsl/