* Li(2,x) now evaluates for +-I.

* Fixed bug in Li(n,x) (if Li(2,x) was calculated with high precision the
  enlargement of the look-up table caused a segmentation fault).

diff --git a/ginac/inifcns_nstdsums.cpp b/ginac/inifcns_nstdsums.cpp
index 94d0fb0c1d3af9442977375b4f90120c972a0b1f..73792b947853a8f25b7d7e18aa1340d9b0379c93 100644 (file)
--- a/ginac/inifcns_nstdsums.cpp
+++ b/ginac/inifcns_nstdsums.cpp
@@ -192,7 +192,7 @@ void double_Xn()
        for (int i=1; i<=xninitsizestep/2; ++i) {
                Xn[0].push_back(bernoulli((i+pos0)*2).to_cl_N());
        }
-       if (Xn.size() > 0) {
+       if (Xn.size() > 1) {
                int xend = xninitsize + xninitsizestep;
                cln::cl_N result;
                // X_1
@@ -397,7 +397,16 @@ numeric Li_num(int n, const numeric& x)
                // [Kol] (2.22)
                return -(1-cln::expt(cln::cl_I(2),1-n)) * cln::zeta(n);
        }
-       
+       if (abs(x.real()) < 0.4 && abs(abs(x)-1) < 0.01) {
+               cln::cl_N x_ = ex_to<numeric>(x).to_cl_N();
+               cln::cl_N result = -cln::expt(cln::log(x_), n-1) * cln::log(1-x_) / cln::factorial(n-1);
+               for (int j=0; j<n-1; j++) {
+                       result = result + (S_num(n-j-1, 1, 1).to_cl_N() - S_num(1, n-j-1, 1-x_).to_cl_N())
+                               * cln::expt(cln::log(x_), j) / cln::factorial(j);
+               }
+               return result;
+       }
+
        // what is the desired float format?
        // first guess: default format
        cln::float_format_t prec = cln::default_float_format;
@@ -574,6 +583,14 @@ static ex Li_eval(const ex& m_, const ex& x_)
                if (m == _ex1) {
                        return -log(1-x);
                }
+               if (m_ == _ex2) {
+                       if (x_.is_equal(I)) {
+                               return power(Pi,_ex2)/_ex_48 + Catalan*I;
+                       }
+                       if (x_.is_equal(-I)) {
+                               return power(Pi,_ex2)/_ex_48 - Catalan*I;
+                       }
+               }
                if (m.info(info_flags::posint) && x.info(info_flags::numeric) && (!x.info(info_flags::crational))) {
                        return Li_num(ex_to<numeric>(m).to_int(), ex_to<numeric>(x));
                }