From: pver@nemdev11 (Peter Verthez)
Newsgroups: sci.math
Subject: Lagrange's Inversion Formula
Date: 22 Feb 1996 06:27:05 GMT

I encountered the following remarkable formula in The Art Of 
Computer Programming (vol.1) by Knuth.  Unfortunately no proof 
or hint of proof was given. 

Given z = t / f(t)   with f(0) not equal to 0
                     and  f(t) analytical around 0

         inf
          --  1   (n-1)     n                      n
then  t = \  --- g     (0) z      with g (t) = f(t)
          /   n!  n                     n
          --
         n=0

Does anyone know how to prove this ? Method only is ok, details
are not necessary.

Thanks in advance,
__________________________________________________________________________
Peter Verthez                                            Software Engineer 
Email: at work                                     pver@bsg.bel.alcatel.be
       at home                                     pver@innet.be
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