Depending on the order formula_3, the polylogarithm may be multi-valued. The "principal branch" of formula_12 is taken to be given for formula_13 by the above series definition and taken to be continuous except on the positive real axis, where a cut is made from formula_14 to formula_15 such that the axis is placed on the lower half plane of formula_16. In terms of formula_17, this amounts to formula_18. The discontinuity of the polylogarithm in dependence on formula_17 can sometimes be confusing.