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Re: Re: InverseFunction[]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg42033] Re: [mg41997] Re: InverseFunction[]
  • From: Sseziwa Mukasa <mukasa at jeol.com>
  • Date: Tue, 17 Jun 2003 05:43:01 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

On Monday, June 16, 2003, at 03:57 AM, Murray Eisenberg wrote:

> No, "?ProductLog" certainly does NOT answer my question!  It tells what
> ProductLog DOES, not how that function is actually computed in
> Mathematica, i.e., what it IS in that sense!
>
> Does Mathematica have some InterpolatingFunction form stored for
> ProductLog?  Does it calculate values of it on the fly by using an
> NDSolve (on the differential equation that the documentation about the
> function mentions)?  Something else?  What?
>

The specific algorithm Mathematica uses is not  hinted at in the 
documentation.  I am not sure why you'd want to know, are you similarly 
curious about how Mathematica computes numerical approximations to 
trigonometric functions?  However, the paper "On the Lambert W 
Function" by Corless, Gonnet, Hare, Jeffrey and Knuth available at 
http://www.apmaths.uwo.ca/~djeffrey/offprints.html contains algorithms 
for the numerical approximation of the ProductLog function.  The paper 
"A Sequence of Series for the Lambert W Function" also available at the 
same site contains a variety of other representations of the ProductLog 
function.

Regards,

Sseziwa

PS - This 


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