Henri . Cohen on Wed, 26 Apr 2006 11:48:50 +0200

 Log. integral

I am not sure this answers Bill Purvis's question but for $x$ not too large
you have the convergent series
$$\Li(x)=\gamma+\log(\log(x))+\sum_{n\ge1}\log(x)^n/(n.n!)$$

H. C.