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
- References:
- Getting rid of ProductLog
- From: robert.hulme@gmail.com (Robert Hulme)
- Getting rid of ProductLog