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Terminology

The notation convention chosen here (with W and W) follows the canonical reference on the Lambert W function by Corless, Gonnet, Hare, Jeffrey and Knuth.

The name "product logarithm" can be understood as this: Since the inverse function of f (w) = e is called the logarithm, it makes sense to call the inverse "function" of the product we as "product logarithm". (Technical note: like the complex logarithm, it is multivalued and thus W is described as the converse relation rather than inverse function.) It is related to the omega constant, which is equal to W (1).