Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What Product Log Means?

  1. Jul 4, 2010 #1
    What Product Log Means??

    Hi,

    I have the following equation:

    B = (k*a*Exp[-t*(B/N)*T/beta] - N)/(a*Exp[-t*(B/N)*T/beta])

    Using Mathematica, I tried to solve it for B. Mathematica returned the following solution:

    B = k-(N*beta*ProductLog[(E^((k*t*T)/(N*beta))*t*T)/(a*beta)])/(t*T)

    What that means? What is ProductLog? How can I have a closed-form expression of that?

    Thanks a lot,

    Estêvão
     
  2. jcsd
  3. Jul 4, 2010 #2

    Mark44

    Staff: Mentor

  4. Jul 4, 2010 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: What Product Log Means??

    "Product log" is also known as the "Lambert W function", the inverse function to [itex]f(x)= xe^x[/itex].
     
  5. Jul 4, 2010 #4
    Re: What Product Log Means??

    Thank you, guys, but I have to tell you: I'm really a begginer in math issues... Therefore, Wolfram Reference's definition and HallsofIvy's definition are still not sufficiently clear to me. Would you give some explanation of "Product Log for Dummies" kind? For example, Wolfram's text simply says that:

    "ProductLog[z]
    gives the principal solution for w in z=w*e^w"

    But what that means? What "w" means? If I have something like:

    ProductLog[(E^((k*t*T)/(N*beta))*t*T)/(a*beta)]

    how can I transform that in a closed-form expression?

    Thanks again,

    Estêvão
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: What Product Log Means?
  1. Whats log? (Replies: 5)

  2. Log of Product (Replies: 3)

Loading...