# Command: LambertW0

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Name:

    LambertW0 - principal branch of the Lambert-W function

Synopsis:

      double LambertW0 -> double

Examples:

      The Lambert-W function has applications in many areas as described in [1] and [3].
      For example, the solution of
      exp(s) = 1 + a*s
      with respect to s can be written in closed form as
      s=1/a * (-aW(-exp(-1/a)/a) -1 )

      Version: 090818

Description:

      The Lambert-W function [1] is the inverse function of x=W*exp(W). For real values of
      x and W, the function W(x) is defined on [-1/e,\infty). On the interval [-1/e,0)
      it is double valued. The two branches coincide at W(-1/e)=-1. The so called
      principal branch LambertW0 continuously grows (W>=-1) and crosses the origin (0,0).
      The non-principal branch LambertWm1 is defined on [-1/e,0) and declines to -\infty for
      growing x.

      NEST uses the GSL [2] implementations of LambertW0 and LambertWm1 if available and
      falls back to to the iterative scheme LambertW suggested in [1] if not.
      The GSL interfaces for LambertW0 and LambertWm1 are in the SpecialFunctionsModule
      of SLI.

References:

      [1] Corless, R. M., Gonnet, G. H., Hare, D. E. G., Jeffrey, D. J., & Knuth, D. E.
      (1996). On the lambert w function. Advances in Computational Mathematics 5,
      329--359.
      [2] Galassi, M., Davies, J., Theiler, J., Gough, B., Jungman, G., Booth, M.,
      & Rossi, F. (2006). GNU Scientific Library Reference Manual (2nd Ed.).
      Network Theory Limited.
      [3] Wikipedia (2009). Lambert W function ---wikipedia, the free encyclopedia.

Author:

    Diesmann

SeeAlso:

- LambertWm1
- LambertW
- testsuite::test_lambertw

Source:

    /opt/conda/conda-bld/nest_1510212701067/work/nest-2.14.0/lib/sli/mathematica.sli

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