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Resultant-Free Computation of Indefinite Hyperexponential Integrals

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Computer Mathematics

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Abstract

In this note, we describe a special structure of differential Gosper forms of rational functions, which allows us to design a new and simple algorithm for constructing differential Gosper forms without the resultant computation and integer-root finding. Moreover, we present an algorithm for computing a universal denominator of the first-order linear differential equation which the Almkvist–Zeilberger algorithm solves.

This work was partially supported by the Tian Yuan Special Funds of the National Natural Science Foundation of China (Grant No. 11126089).

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Acknowledgments

The author would like to thank the anonymous referees for their constructive and helpful comments.

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Authors and Affiliations

  1. The School of Science, Hangzhou Dianzi University, Hangzhou, 310018, Zhejiang, China

    Xiaoli Wu

  2. Key Laboratory of Mathematics Mechanization, Chinese Academy of Sciences, Beijing, 100190, China

    Xiaoli Wu

Authors
  1. Xiaoli Wu
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Correspondence to Xiaoli Wu .

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Editors and Affiliations

  1. Academy of Mathematics & System Science, Beijing, China

    Ruyong Feng

  2. Department of Mathematics and Computer S, University of Antwerp, Antwerp, Antwerpen, Belgium

    Wen-shin Lee

  3. Department of Mathematical Information S, Tokyo University of Science, Tokyo, Tokyo, Japan

    Yosuke Sato

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Wu, X. (2014). Resultant-Free Computation of Indefinite Hyperexponential Integrals. In: Feng, R., Lee, Ws., Sato, Y. (eds) Computer Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43799-5_28

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