Gamma detector dead time correction using Lambert W function

The Lambert W Function

has a countably infinite number of solutions, which are denoted by Wk(z) for integers k. Each choice of k specifies a branch of the Lambert W function. By convention, only the branches k = 0 (called the principal branch) and k = −1 are real-valued for any z; the range of every other branch excludes the real axis, although the range of W1(z) includes (−∞,−1/e] in its closure. Only W0(z) contains...

Lambert W Function in Hydraulic Problems ∗

Darcy’s flow friction factor is expressed in implicit form in some of the relations such as Colebrook’s and have to be solved by iteration procedure because the unknown friction factor appears on both sides of the equation. Lambert W function is implicitly elementary but is not, itself, an elementary function. Implicit form of the Lambert W function allows us to transform other implicit functio...

Having Fun with Lambert W(x) Function

This short note presents the Lambert W(x) function and its possible application in the framework of physics related to the Pierre Auger Observatory. The actual numerical implementation in C++ consists of Halley’s and Fritsch’s iteration with branch-point expansion, asymptotic series and rational fits as initial approximations. ar X iv :1 00 3. 16 28 v1 [ cs .M S] 8 M ar 2 01 0

Lambert W Function for Applications in Physics

The Lambert W(x) function and its possible applications in physics are presented. The actual numerical implementation in C++ consists of Halley’s and Fritsch’s iterations with initial approximations based on branch-point expansion, asymptotic series, rational fits, and continued-logarithm recursion.

Time-delay Systems: Analysis and Control Using the Lambert W Function