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The notation convention chosen here (with W 0 and W −1) follows the canonical reference on the Lambert W function by Corless, Gonnet, Hare, Jeffrey and Knuth. [3]The name "product logarithm" can be understood as follows: since the inverse function of f(w) = e w is termed the logarithm, it makes sense to call the inverse "function" of the product we w the "product logarithm".
One problem with p/m or +/- is that it is limited to only two branches, but the numerical subscript allows indexing all branches of the Lambert W function (this article fails to note this). The "old" notation is also used in computer algebra systems, which are the most important domain of use for the Lambert W function.
Notation ( , ) ... is the Lambert W function. This approximation is derived via an asymptotic method, but it stays sharp all over the domain of convergence of ...
It is the value of W(1), where W is Lambert's W function. The name is derived from the alternate name for Lambert's W function, the omega function. The numerical value of Ω is given by Ω = 0.56714 32904 09783 87299 99686 62210... (sequence A030178 in the OEIS). 1/Ω = 1.76322 28343 51896 71022 52017 76951... (sequence A030797 in the OEIS).
where W represents Lambert's W function. As the limit y = ∞ x (if existent on the positive real line, i.e. for e −e ≤ x ≤ e 1/e) must satisfy x y = y we see that x ↦ y = ∞ x is (the lower branch of) the inverse function of y ↦ x = y 1/y.
As you see, it doesn't seem so theoretically relevant to deserve an article of its own; but as a notation is nice and of some use. --pm a 19:08, 17 February 2010 (UTC) It is also used in loads of other places like removing parts of a graph or when reasoning about computer floating point where there is a vaguely subtraction type of operator and ...
The Lambert W function is the function () that is implicitly defined by the equation () =. We may use the theorem to compute the Taylor series of () at ...
W represents: the unit watt of power [10] work, both mechanical and thermodynamical [23]: 8–9 in thermodynamics, the number of possible quantum states in Boltzmann's entropy formula; weight measured in newtons [10] Lambert's W function [33] Tungsten; W boson; Work function; Wiener process; w represents: the coordinate on the fourth axis in ...