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Series Transformations to Improve and Extend Convergence

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Book cover Computer Algebra in Scientific Computing (CASC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6244))

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Abstract

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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References

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Authors and Affiliations

  1. Department of Applied Mathematics, The University of Western Ontario, London, Ontario, Canada

    G. A. Kalugin & D. J. Jeffrey

Authors
  1. G. A. Kalugin
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  2. D. J. Jeffrey
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Editor information

Editors and Affiliations

  1. JINR, Moscow region, 141980, Dubna, Russia

    Vladimir P. Gerdt

  2. University of Kassel, 34109 l, Kasse, Germany

    Wolfram Koepf

  3. Technische Universität München, 85748, Garching, Germany

    Ernst W. Mayr

  4. Russian Academy of Sciences,, 630090, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Kalugin, G.A., Jeffrey, D.J. (2010). Series Transformations to Improve and Extend Convergence. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2010. Lecture Notes in Computer Science, vol 6244. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15274-0_12

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  • DOI: https://doi.org/10.1007/978-3-642-15274-0_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15273-3

  • Online ISBN: 978-3-642-15274-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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