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Integration in finite terms: dilogarithmic integrals

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

We extend the theorem of Liouville on integration in finite terms to include dilogarithmic integrals. The results provide a necessary and sufficient condition for an element of the base field to have an antiderivative in a field extension generated by transcendental elementary functions and dilogarithmic integrals.

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Notes

  1. We no longer require that \(C_F\) is an algebraically closed field or that F is a liouvillian extension of \(C_F\).

  2. We thank the anonymous referee of [3] for pointing this out to us.

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Authors and Affiliations

  1. Mathematics Department, IISER Pune, Pune, India

    Yashpreet Kaur

  2. Department of Mathematical Sciences, IISER Mohali, Mohali, India

    Varadharaj R. Srinivasan

Authors
  1. Yashpreet Kaur
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  2. Varadharaj R. Srinivasan
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Correspondence to Varadharaj R. Srinivasan.

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Kaur, Y., Srinivasan, V.R. Integration in finite terms: dilogarithmic integrals. AAECC 34, 539–551 (2023). https://doi.org/10.1007/s00200-021-00518-3

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  • DOI: https://doi.org/10.1007/s00200-021-00518-3

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