# logarithmic integral

## Primary tabs

Defines:
logarithmic integral, logarithmus integralis, Eulerian logarithmic integral
Synonym:
Li
Type of Math Object:
Definition
Major Section:
Reference
Groups audience:

## Mathematics Subject Classification

### Pole or essential singularity?

Hi, I am unsure whether z = 1 is a pole or an essential singularity of the logarithmic integral. It is clear that z = 1 is a pole of order 1 of 1/ln{z}.
Jussi

### Re: Pole or essential singularity?

Neither --- it is a branch point. When one integrates a simple pole,
one genrates a logarithm. you can think of it this way. Write
1/ln{z} as 1/(z-1) + f(z) where f is analytic at z = 1 (in other
words, separate out the pole). Integrating, we find that li{z} =
log (z-1) + F(z), where F is the antiderivative of f, which makes it
analytic at z = 1.

### Re: Pole or essential singularity?

Thank you, Ray! Thus I must remove the attribute "meromorphic" from the entry.
Jussi