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MathGroup Archive 2004

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Re: Getting rid of ProductLog

  • To: mathgroup at
  • Subject: [mg49236] Re: [mg49230] Getting rid of ProductLog
  • From: Sseziwa Mukasa <mukasa at>
  • Date: Fri, 9 Jul 2004 02:26:07 -0400 (EDT)
  • References: <>
  • Sender: owner-wri-mathgroup at

On Jul 8, 2004, at 2:51 AM, Robert Hulme wrote:

> Hi,
> Could someone please help me?
> I'm not a mathematician, but rather a programmer - I'm trying to use
> Mathematica to rearrange a formula for me.
> I'm trying:
> Solve[a^b - b == c, b]
> Which gives me:
> Out[3]//TextForm=
>                          Log[a]
>             ProductLog[-(------)]
>                             c
>                            a
> {{b -> -c - ---------------------}}
>                    Log[a]
> The problem with this is that I need the solution to use normal
> 'primitive' (if thats the right word) math functions as I need the
> formula for a computer program.
> With ProductLog being an internal Mathematica function I cant
> therefore use this rearrangement.
> What can I do so that there is no ProductLog in there? Please go easy
> on me as I'm not a math major :0) or that au fait with Mathematica.
> If it helps both a and b are always positive.

ProductLog is also known as the Lambert W function.  You can find a 
description of it here  There are a 
couple of asymptotic series and an approximation of W(x) for x>=3 
given.  Knuth and Robert Corless published a few papers on the function 
which a listed here  Algorithm 
443 of the Communications of the ACM is supposed to evaluate Lambert's 
W for the principle branch and positive real arguments.  For a > e 
however your argument is going to be negative, apparently Algorithm 443 
can be extended to account for this according to Corless.  Note that 
W(z) is complex valued for z<0.



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