3.5.1.3.55 lambertWLambertW-func
Definition:
The lambertW(x[, branch, offset]) function calculates an approximate value for the real branches of Lambert’s W function
(sometimes known as the ‘product log’ or ‘Omega’ function), which is the inverse function of
/math-118ed99068a74add6905a246d8fa9d06.png?v=0 "f\left ( w \right )=we^{w}") for /math-23198167ffd1f62fc2d26ebad9d0d4e5.png?v=0 "w \in C")
The function f is many-to-one, and so, except at 0, W is multivalued.
This labtalk function is implemented from NAG9(c05bac), you may refer to detailed information in the NAG library.
Parameters:
x
- The value if offset is not chosen, or the offset
/math-b56546a86ab832a9b2a5b15f96519319.png?v=0 "\Delta x") from /math-aa8be46c9b9afb3f0b174eee2b85fbe6.png?v=0 "-exp\left ( -1 \right )") of the intended argument to W if the offset is chosen.
branch
- Optional. The real branch required, should be 0 or -1.
offset
- Optional. Controls whether or not x is being specified as an offset from , should be 0 or 1.
Examples:
lambertW(0.25)=0.203888
lambertW(0.5, 0, 0) = 0.351734
lambertW(0.75, 0, 1) = 0.286834
lambertW(-0.25, -1, 0) = -2.153292
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