All Questions
3
questions
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 $...
- 6,277
3
votes
0
answers
75
views
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 ...
- 6,280
1
vote
1
answer
1k
views
on the (double) discontinuity of dilogarithm along a branch cut
Define the function
$$Li_s(z)=\sum_{k=1}^\infty \frac{z^k}{k^s}$$
for |z|<1. Let's focus on $s=2$.
It can be extended to a holomorphic function on $\mathbb C \setminus [1,\infty)$
$$Li_2(z)= -\...
- 2,390