Advances in Computational Mathematics

, Volume 5, Issue 1, pp 329–359

On the LambertW function

  • R. M. Corless
  • G. H. Gonnet
  • D. E. G. Hare
  • D. J. Jeffrey
  • D. E. Knuth
Article

Abstract

The LambertW function is defined to be the multivalued inverse of the functionwwew. It has many applications in pure and applied mathematics, some of which are briefly described here. We present a new discussion of the complex branches ofW, 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 containingW.

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Copyright information

© J.C. Baltzer AG, Science Publishers 1996

Authors and Affiliations

  • R. M. Corless
    • 1
  • G. H. Gonnet
    • 2
  • D. E. G. Hare
    • 3
  • D. J. Jeffrey
    • 1
  • D. E. Knuth
    • 4
  1. 1.Department of Applied MathematicsUniversity of Western OntarioLondonCanada
  2. 2.Institut für Wissenschaftliches RechnenETHZürichSwitzerland
  3. 3.Symbolic Computation GroupUniversity of WaterlooWaterlooCanada
  4. 4.Department of Computer ScienceStanford UniversityStanfordUSA

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