Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2004
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2004

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Getting rid of ProductLog

  • To: mathgroup at smc.vnet.net
  • Subject: [mg49236] Re: [mg49230] Getting rid of ProductLog
  • From: Sseziwa Mukasa <mukasa at jeol.com>
  • Date: Fri, 9 Jul 2004 02:26:07 -0400 (EDT)
  • References: <200407080651.CAA04104@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

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 
http://mathworld.wolfram.com/LambertW-Function.html.  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 
http://www.apmaths.uwo.ca/~rcorless/frames/PAPERS/LambertW/.  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.

Regards,

Ssezi


  • Prev by Date: Re: Getting rid of ProductLog
  • Next by Date: Re: Normal distribtion
  • Previous by thread: Getting rid of ProductLog
  • Next by thread: Re: Getting rid of ProductLog