Series Transformations to Improve and Extend Convergence

  • G. A. Kalugin
  • D. J. Jeffrey
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6244)


We consider a new invariant transformation of some previously known series for the Lambert W function. The transformations contain a parameter p which can be varied, while retaining the basic series structure. The parameter can be used to expand the domain of convergence of the series. The speed of convergence, that is the accuracy for a given number of terms, can increase or decrease with p. Theoretical and experimental investigations that rely heavily on the computer-algebra system Maple are described.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • G. A. Kalugin
    • 1
  • D. J. Jeffrey
    • 1
  1. 1.Department of Applied MathematicsThe University of Western OntarioLondonCanada

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