Re: best approximation to the LambertW(x) or exp(LambertW(x)) for large x say x > 2500
- To: mathgroup at smc.vnet.net
- Subject: [mg117138] Re: best approximation to the LambertW(x) or exp(LambertW(x)) for large x say x > 2500
- From: Scott Hemphill <hemphill at hemphills.net>
- Date: Thu, 10 Mar 2011 06:12:47 -0500 (EST)
- References: <il7qab$du5$1@smc.vnet.net>
- Reply-to: hemphill at alumni.caltech.edu
barefoot gigantor <barefoot1980 at gmail.com> writes: > what is the best available approximation ( say up to 10 digits ) for > LambertW(x) or exp(LambertW(x)) for x > 2000 > > thank you for your help It isn't immediately obvious to me what "best" means. You are solving for x in the equation y == x * E^x. A simple solution would be to start with x = Log[y], then iterate x = Log[y] - Log[x] enough times that you have as many correct digits as you need. The convergence is a little slow, though, so you could use Newton's Method instead. You could still start with x = Log[y], but then iterate x = (Log[y]-Log[x]+1) * x/(x+1). Scott -- Scott Hemphill hemphill at alumni.caltech.edu "This isn't flying. This is falling, with style." -- Buzz Lightyear