Lambert - dimensions of dreams - Lambert W function - Wikipedia


Since the function ƒ is not injective , the relation W is multivalued (except at 0). If we restrict attention to real-valued W , the complex variable z is then replaced by the real variable x , and the relation is defined only for x  ≥ −1/ e , and is double-valued on (−1/ e , 0). The additional constraint W ≥ −1 defines a single-valued function W 0 ( x ). We have W 0 (0) = 0 and W 0 (−1/ e ) = −1. Meanwhile, the lower branch has W ≤ −1 and is denoted W −1 ( x ). It decreases from W −1 (−1/ e ) = −1 to W −1 (0 − ) = −∞.


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