All Questions
3
questions
2
votes
2
answers
288
views
Does the dilogarithm function (which is multi-valued) have a single-valued inverse?
The $p$-logarithm is defined for $|z|<1$ by
$$\text{Li}_p(z)=\sum_{n=1}^\infty\frac{z^n}{n^p}$$
and defined elsewhere in $\mathbb C$ by analytic continuation, though it may be multi-valued, ...
2
votes
2
answers
797
views
Branch Points of the Polylog function
The polylogarithm
$$
{\rm Li}_s(z) = \sum_{n=1}^\infty \frac{z^n}{n^s}
$$
has obvious branch points at $z=1$.
For integers $s\leq 0$ it is a rational function with a pole of order $1-s$ at $z=1$. If $...
3
votes
0
answers
75
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Approaching a branch point along different paths
There's a very nice characterization of the three main types of isolated singularities of an analytic function $f(z)$ that takes oriented curves $\gamma$ that terminate at the singularity and ...