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Linear Differential Systems with Infinite Power Series Coefficients (Invited Talk)

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Computer Algebra in Scientific Computing (CASC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10490))

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Abstract

Infinite power series may appear as inputs for certain mathematical problems. This paper examines two possible solutions to the problem of representation of infinite power series: the algorithmic representation (for each series, an algorithm is specified that, given an integer i, finds the coefficient of \(x^i\), — any such algorithm defines a so called computable, or constructive, series) and a representation in an approximate form, namely, in a truncated form.

S.A. Abramov—Supported in part by the Russian Foundation for Basic Research, project No. 16-01-00174.

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Acknowledgments

The author is thankful to M. Barkatou, D. Khmelnov, M. Petkovšek, E. Pflügel, A. Ryabenko and M. Singer for valuable discussions.

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Authors and Affiliations

  1. Dorodnitsyn Computing Centre, Federal Research Center Computer Science and Control of Russian Academy of Sciences, Vavilova, 40, Moscow, 119333, Russia

    S. A. Abramov

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  1. S. A. Abramov
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Correspondence to S. A. Abramov .

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Editors and Affiliations

  1. Joint Institute of Nuclear Research, Dubna, Russia

    Vladimir P. Gerdt

  2. Universität Kassel, Kassel, Germany

    Wolfram Koepf

  3. Universität Kassel, Kassel, Germany

    Werner M. Seiler

  4. Russian Academy of Sciences, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Abramov, S.A. (2017). Linear Differential Systems with Infinite Power Series Coefficients (Invited Talk). In: Gerdt, V., Koepf, W., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2017. Lecture Notes in Computer Science(), vol 10490. Springer, Cham. https://doi.org/10.1007/978-3-319-66320-3_1

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  • DOI: https://doi.org/10.1007/978-3-319-66320-3_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66319-7

  • Online ISBN: 978-3-319-66320-3

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