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On the Lambert w function. (English) Zbl 0863.65008
The tree function T defined by series T(v)=v+2 2!v 2 +3 2 3!v 3 +4 3 4!v 4 + converges for |v|<1 e. It equals -w(-v), where w(z) is defined to be the function satisfying w(z)e w(z) =z. This paper discusses both w and T, concentrating on w. The authors present a new discussion of the complex branches for w, an asymptotic expansion valid for all branches, an efficient numerical procedure for evaluating the function to arbitrary precision, and a method for the symbolic integration of expressions containing w.

65E05Numerical methods in complex analysis
30E10Approximation in the complex domain
65D20Computation of special functions, construction of tables
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