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Lambaert W numbers

  1. Jan 28, 2012 #1
    Lambert W *edit*

    How are these numbers calculated let's say W(5.67)
     
    Last edited: Jan 28, 2012
  2. jcsd
  3. Jan 28, 2012 #2

    I like Serena

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    Welcome to PF, mabauti! :smile:

    You can calculate W(5.67) for instance with WolframAlpha:
    http://www.wolframalpha.com/input/?i=W(5.67)


    W can only be calculated by a numerical algorithm.
    The Wolfram article about the Lambert W function gives a couple of series expansions that you can use:
    http://mathworld.wolfram.com/LambertW-Function.html


    You could also approximate it with for instance the Newton-Raphson method with ##f(x)=xe^x - 5.67=0##.
    That is: ##x_{k+1}=x_k - {f(x_k) \over f'(x_k)}##.
    Start with ##x_0=2## and you should be able to find your result to an arbitrary precision within a couple of iterations.
     
  4. Jan 28, 2012 #3
    great.

    thanks ILS =D
     
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