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dilog and spence


I just put some fixes in CVS. The dilog functions
should be working ok. If there are still problems,
please show me how catch them with the tests. There
are now tests in place which should cover the bad
regions which were discussed previously. But please
check.

I have also added a function

  gsl_sf_spence_e(
    const double A,
    const double omega,
    gsl_sf_result * real_sp,
    gsl_sf_result * imag_sp
  );

which computes spence(s) := Li_2(1-s), but uses
the representation s = A exp(i omega) to resolve
the branch, i.e. to compute on the full Riemann
surface. This implementation is preliminary, and
there are essentially no tests. I expect it to
work correctly on the principle branch, but the
behavior on the other sheets needs to be checked.
I don't currently have a way to check those, so
I am crossing my fingers that I did the algebra
correctly. It would be helpful if somebody
could provide test values for the other branches.

Thanks.

--
G. Jungman


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