- // if we got here we have to care for cuts and poles
- return (log((1+x)/(1-x))/2).series(rel, order, options);
+ // care for the poles, using the defining formula for atanh()...
+ if (arg_pt.is_equal(_ex1) || arg_pt.is_equal(_ex_1))
+ return ((log(_ex1+arg)-log(_ex1-arg))*_ex1_2).series(rel, order, options);
+ // ...and the branch cuts (the discontinuity at the cut being just I*Pi)
+ if (!(options & series_options::suppress_branchcut)) {
+ // method:
+ // This is the branch cut: assemble the primitive series manually and
+ // then add the corresponding complex step function.
+ const symbol &s = ex_to<symbol>(rel.lhs());
+ const ex point = rel.rhs();
+ const symbol foo;
+ const ex replarg = series(atanh(arg), s==foo, order).subs(foo==point);
+ ex Order0correction = replarg.op(0)+csgn(I*arg)*Pi*I*_ex1_2;
+ if (arg_pt<_ex0)
+ Order0correction += log((arg_pt+_ex_1)/(arg_pt+_ex1))*_ex1_2;
+ else
+ Order0correction += log((arg_pt+_ex1)/(arg_pt+_ex_1))*_ex_1_2;
+ epvector seq;
+ seq.push_back(expair(Order0correction, _ex0));
+ seq.push_back(expair(Order(_ex1), order));
+ return series(replarg - pseries(rel, seq), rel, order);
+ }
+ throw do_taylor();