Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

It is shown here on Mathworld's page on Stirling number of the second kind that

$$ \sum_{k=1}^n S(n,k) (k-1)! z^k = (-1)^n \text{Li}_{1-n}(1+\frac{1}{z}) $$

where $S(n,k)$ is Stirling number of the second kind and $\text{Li}_{1-n}$ is the polylogarithm.

Can somebody provide me some reference on where this identity came from? It isn't shown on Mathworld's page.

share|improve this question
    
Unless I am mistaken, this seems to simply the result of a Lagrange inversion of a series for the polylog function (see the Wikipedia page for the series for Li that is a candidate). –  Suvrit Mar 11 '12 at 18:04
add comment

1 Answer

up vote 3 down vote accepted

See Steven Landsburg's note.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.