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Math Help - The product log is not elementary

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    The product log is not elementary

    The product logarithm (Lambert W) is the inverse of f(z) = z e^z. Wikipedia claims it is not elementary, but gives no reference. How do we know that is not elementary?
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    Quote Originally Posted by maddas View Post
    The product logarithm (Lambert W) is the inverse of f(z) = z e^z. Wikipedia claims it is not elementary, but gives no reference. How do we know that is not elementary?

    You can read a proof here: Algebraic properties of the Lambert W function from a result of Rosenlicht and of Liouville - Integral Transforms and Special Functions

    It is not trivial, or even easy.

    Tonio
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