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International Conference on Mathematical Aspects of Computer and Information Sciences

MACIS 2017: Mathematical Aspects of Computer and Information Sciences pp 270–274Cite as

Rapidly Convergent Integrals and Function Evaluation

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10693))

Abstract

We analyse integrals representing the Lambert W function, paying attention to computations using various rules. Rates of convergence are investigated, with the way in which they vary over the domain of the function being a focus. The first integral evaluates with errors independent of the function variable over a significant range. The second integral converges faster, but the rate varies with the function variable.

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Notes

  1. 1.

    Maple programmers will be jumping to improve this code for style and efficiency, but the issue is rate of convergence, not programming efficiency, and the code reflects the algorithm as given in [2].

References

  1. Corless, R.M., Gonnet, G.H., Hare, D.E.G., Jeffrey, D.J., Knuth, D.E.: On the Lambert W function. Adv. Comput. Math. 5, 329–359 (1996)

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  2. Iacono R., Boyd, J.P.: New approximations to the principal real-valued branch of the Lambert W-function. Adv. Comput. Math., 1–34 (2017)

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  4. Kalugin, G.A., Jeffrey, D.J., Corless, R.M., Borwein, P.B.: Stieltjes and other integral representations for functions of Lambert W. Integr. Transforms Spec. Functions 23(8), 581–593 (2012). https://doi.org/10.1080/10652469.2011.613830

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  5. Poisson, S.-D.: Suite du mémoire sur les intégrales définies et sur la sommation des séries. J. de l’École Royale Polytechnique 12, 404–509 (1823)

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, The University of Western Ontario, London, ON, N6G 2B3, Canada

    Heba al Kafri, David J. Jeffrey & Robert M. Corless

Authors
  1. Heba al Kafri
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  2. David J. Jeffrey
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  3. Robert M. Corless
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Corresponding author

Correspondence to David J. Jeffrey .

Editor information

Editors and Affiliations

  1. University of Paderborn, Paderborn, Germany

    Johannes Blömer

  2. Wilfrid Laurier University, Waterloo, Ontario, Canada

    Ilias S. Kotsireas

  3. Johannes Kepler University Linz, Linz, Austria

    Temur Kutsia

  4. SBA Research, Vienna, Austria

    Dimitris E. Simos

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Cite this paper

al Kafri, H., Jeffrey, D.J., Corless, R.M. (2017). Rapidly Convergent Integrals and Function Evaluation. In: Blömer, J., Kotsireas, I., Kutsia, T., Simos, D. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2017. Lecture Notes in Computer Science(), vol 10693. Springer, Cham. https://doi.org/10.1007/978-3-319-72453-9_20

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  • DOI: https://doi.org/10.1007/978-3-319-72453-9_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-72452-2

  • Online ISBN: 978-3-319-72453-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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