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Published in: Applicable Algebra in Engineering, Communication and Computing 4/2023

16-06-2021 | Original Paper

Integration in finite terms: dilogarithmic integrals

Authors: Yashpreet Kaur, Varadharaj R. Srinivasan

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 4/2023

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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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Footnotes
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.
 
Literature
1.
3.
go back to reference Kaur, Y., Srinivasan, V.: Integration in finite terms with dilogarithmic integrals, logarithmic integrals and error functions. J. Symb. Comput. 94, 210–233 (2019)MathSciNetCrossRefMATH Kaur, Y., Srinivasan, V.: Integration in finite terms with dilogarithmic integrals, logarithmic integrals and error functions. J. Symb. Comput. 94, 210–233 (2019)MathSciNetCrossRefMATH
5.
8.
go back to reference Singer, M., Saunders, B., Caviness, B.: An extension of Liouville’s theorem on integration in finite terms. SIAM J. Comput. 14(4), 966–990 (1985)MathSciNetCrossRefMATH Singer, M., Saunders, B., Caviness, B.: An extension of Liouville’s theorem on integration in finite terms. SIAM J. Comput. 14(4), 966–990 (1985)MathSciNetCrossRefMATH
Metadata
Title
Integration in finite terms: dilogarithmic integrals
Authors
Yashpreet Kaur
Varadharaj R. Srinivasan
Publication date
16-06-2021
Publisher
Springer Berlin Heidelberg
Published in
Applicable Algebra in Engineering, Communication and Computing / Issue 4/2023
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-021-00518-3

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