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