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Representations of Numbers as \(\sum_{k=-n}^n \varepsilon_k k\):A Saddle Point Approach

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Infinity in Logic and Computation (ILC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5489))

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Abstract

Using the saddle point method, we obtain from the generating function of the numbers in the title and Cauchy’s integral formula asymptotic results of high precision in central and non-central regions.

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References

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Author information

Authors and Affiliations

  1. Département d’Informatique, Université Libre de Bruxelles, CP 212,Boulevard du Triomphe, 1050, Bruxelles, Belgium

    Guy Louchard

  2. Mathematics Department, University of Stellenbosch, 7602, Stellenbosch, South Africa

    Helmut Prodinger

Authors
  1. Guy Louchard
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  2. Helmut Prodinger
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Cape Town, 7701, Rondebosch, South Africa

    Margaret Archibald  & Vasco Brattka  & 

  2. School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa

    Valentin Goranko

  3. Institute for Logic, Language and Computation, Universiteit van Amsterdam, 1090, Amsterdam, GE, The Netherlands

    Benedikt Löwe

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Louchard, G., Prodinger, H. (2009). Representations of Numbers as \(\sum_{k=-n}^n \varepsilon_k k\):A Saddle Point Approach. In: Archibald, M., Brattka, V., Goranko, V., Löwe, B. (eds) Infinity in Logic and Computation. ILC 2007. Lecture Notes in Computer Science(), vol 5489. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03092-5_7

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  • DOI: https://doi.org/10.1007/978-3-642-03092-5_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03091-8

  • Online ISBN: 978-3-642-03092-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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