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An efficient calculation of the Clausen functions Cl n (θ)(n≥2)

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Abstract

The Clausen functions appear in many problems, such as in the computation of singular integrals, quantum field theory, and so on. In this paper, we consider the Clausen functions Cl n (θ) with n≥2. An efficient algorithm for evaluating them is suggested and the corresponding convergence analysis is established. Finally, some numerical examples are presented to show the efficiency of our algorithm.

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Authors and Affiliations

  1. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088, P.R. China

    Jiming Wu

  2. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, P.R. China

    Xiaoping Zhang

  3. Department of Mathematics, College of Sciences, Shanghai University, Shanghai, 200444, P.R. China

    Dongjie Liu

Authors
  1. Jiming Wu
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  2. Xiaoping Zhang
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  3. Dongjie Liu
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Corresponding author

Correspondence to Xiaoping Zhang.

Additional information

Communicated by Lothar Reichel.

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Wu, J., Zhang, X. & Liu, D. An efficient calculation of the Clausen functions Cl n (θ)(n≥2). Bit Numer Math 50, 193–206 (2010). https://doi.org/10.1007/s10543-009-0246-8

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  • DOI: https://doi.org/10.1007/s10543-009-0246-8

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