Lambert W Function: Calculate W(5.67)

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SUMMARY

The Lambert W function, specifically W(5.67), can be calculated using numerical algorithms such as the Newton-Raphson method. This method involves solving the equation f(x) = xe^x - 5.67 = 0, with an initial guess of x0 = 2. The WolframAlpha tool provides a straightforward way to compute W(5.67) and offers additional resources for understanding the Lambert W function, including series expansions available on Wolfram's MathWorld.

PREREQUISITES
  • Understanding of the Lambert W function
  • Familiarity with numerical methods, specifically the Newton-Raphson method
  • Basic knowledge of exponential functions
  • Experience using computational tools like WolframAlpha
NEXT STEPS
  • Explore the series expansions of the Lambert W function on Wolfram MathWorld
  • Learn the implementation details of the Newton-Raphson method for root-finding
  • Investigate other numerical algorithms for calculating the Lambert W function
  • Practice using WolframAlpha for various inputs to understand its capabilities
USEFUL FOR

Mathematicians, engineers, and anyone involved in numerical analysis or computational mathematics who needs to calculate or understand the Lambert W function.

mabauti
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Lambert W *edit*

How are these numbers calculated let's say W(5.67)
 
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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.htmlYou 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.
 
great.

thanks ILS =D
 

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