Re: best approximation to the LambertW(x) or exp(LambertW(x)) for large x say x > 2500
- To: mathgroup at smc.vnet.net
- Subject: [mg117116] Re: best approximation to the LambertW(x) or exp(LambertW(x)) for large x say x > 2500
- From: Peter Pein <petsie at dordos.net>
- Date: Thu, 10 Mar 2011 06:08:48 -0500 (EST)
Am 09.03.2011 13:03, schrieb barefoot gigantor:
> 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
>
>
Hi,
the series expansion around x0=Infinity seems to fit well:
f=Compile[{{x,_Real}},Simplify[Series[LambertW[x],{x,Infinity,12}]//Normal,x>00]//Evaluate];
Off[CompiledFunction::cfsa]
the absolute error is ~10^-11 or smaller:
LogLogPlot[LambertW[x]-f[x]//Abs,{x,2000,7*^10}]
hth,
Peter