# Polylogarithm and taylor series

1. Dec 6, 2012

### rylz

let nε Z. the polylogarithm functions are a family of functions, one for each n. they are defined by the following taylor series:
Lin(x)= Ʃ xk/kn

3. when i attempted this part, i couldnt use theratio or root test, so by comparison i got R=∞

2. Prove that (1-x)2 Li-1 (x)= x

im not sure how to go about this. i know that Li-1 (x)= 1/(1-x)2 but im not sure how to prove that..........

2. Dec 6, 2012

### Dick

For the first part, I have no idea what you compared with. For the second just look at the taylor series expansion of 1/(1-x)^2. If that's Li-1(x), and it is, it certainly doesn't have radius of convergence ∞.

Last edited: Dec 6, 2012
3. Dec 8, 2012

### rylz

hey! so i sorted out the first part but how do i axctually prove that Li-1 (x) is equal to 1/(1-x)^2?

4. Dec 8, 2012

### Dick

I told you. Find the taylor series expansion of 1/(1-x)^2. Compare it with the series definition of your polylogarithm.