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On Morrison’s definite integral

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Abstract

As an application of Cauchy’s Theorem we prove that

$$\int_{0}^{1}{\rm arctan}\left(\frac{{\rm arctanh} x-{\rm arctan} x}{\pi+{\rm arctanh} x-{\rm arctan} x}\right) \frac{dx}{x}= \frac{\pi}{8}{\rm log}\frac{\pi^{2}}{8}$$

answering by this means a question posted in 1984 by J. A. Morrison in the Problem Section of the journal SIAM Review.

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Authors and Affiliations

  1. Facultad de Matemáticas, Univ. de Sevilla, Apdo. 1160, 41080, Sevilla, Spain

    J. Arias de Reyna

  2. Dpto. de Física Teórica, Facultad de Ciencias, Universidad de Valladolid, Paseo Belén 9, 47011, Valladolid, Spain

    M. L. Glasser

  3. Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, 08544, USA

    Y. Zhou

Authors
  1. J. Arias de Reyna
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  2. M. L. Glasser
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  3. Y. Zhou
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Correspondence to M. L. Glasser.

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Arias de Reyna, J., Glasser, M.L. & Zhou, Y. On Morrison’s definite integral. Aequat. Math. 89, 1241–1250 (2015). https://doi.org/10.1007/s00010-015-0355-1

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  • DOI: https://doi.org/10.1007/s00010-015-0355-1

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