Reducing Hyperexponential Functions over Monomial Extensions

The authors extend the shell and kernel reductions for hyperexponential functions over the field of rational functions to a monomial extension. Both of the reductions are incorporated into one algorithm. As an application, the authors present an additive decomposition in rationally hyperexponential...

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Bibliographic Details
Published inJournal of systems science and complexity Vol. 38; no. 3; pp. 1206 - 1225
Main Authors Chen, Shaoshi, Du, Hao, Gao, Yiman, Li, Ziming
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2025
Springer Nature B.V
Subjects
Algorithms
Complex Systems
Control
Decomposition
Integrals
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research/Decision Theory
Rational functions
Statistics
Systems Theory
Towers
hyperexponential function
symbolic integration
Additive decomposition
reduction
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Summary:The authors extend the shell and kernel reductions for hyperexponential functions over the field of rational functions to a monomial extension. Both of the reductions are incorporated into one algorithm. As an application, the authors present an additive decomposition in rationally hyperexponential towers. The decomposition yields an alternative algorithm for computing elementary integrals over such towers. The alternative can find some elementary integrals that are unevaluated by the integrators in the latest versions of maple and mathematica .
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1009-6124
1559-7067
DOI:10.1007/s11424-024-3325-7