Why is the polylogarithm equation for n=1 a logarithm?

[MathematicalPhysicist]

the equation of pl is:
(infinity)
y= sum x^i/i^n
i=1
in here http://www.2dcurves.com/exponential/exponentialpo.html it states in the case n=1 it is a logarithm i want to know why?

for all of my knowledge it should be y=x/1+x^2/2+x^3/3+...
is this the taylor expansion series for a logarithm?

 

[HallsofIvy]

Not exactly. For one thing that series gives y= 0 when x= 0 and log(x) is not defined for x=0.

The series you give is the Taylor's series for ln(x+1).

 

[MathematicalPhysicist]

so is this what meant in the webpage?