The Lambert W function is the multivalued inverse of , so . Its principal real branch satisfies as .
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The Lambert W function, often denoted as \( W(x) \), is a special function that is defined as the inverse of the function \( f(W) = W e^W \). In other words, if \( W = W(x) \), then: \[ x = W e^W \] This means that the Lambert W function gives solutions \( W \) for equation \( x = W e^W \) for various values of \( x \).