       Re: Getting rid of ProductLog

• To: mathgroup at smc.vnet.net
• Subject: [mg49243] Re: Getting rid of ProductLog
• From: John Doty <jpd at whispertel.LoseTheH.net>
• Date: Fri, 9 Jul 2004 02:26:13 -0400 (EDT)
• References: <ccisbq\$4de\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```You might take a look at http://en.wikipedia.org/wiki/Lambert's_W_function

ProductLog, or W, *is* elementary, in the sense that it cannot be
expressed in terms of more common elementary functions.

If all you want is a numerical solution, it may be easier and faster to
apply a numerical root finding algorithm to your original equation
rather than attempt to numerically evaluate a symbolic solution.

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//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.
>
> Many thanks
> -Rob
>

```

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