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On m-Interlacing Solutions of Linear Difference Equations

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Computer Algebra in Scientific Computing (CASC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5743))

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Abstract

We consider linear homogeneous difference equations with rational-function coefficients. The search for solutions in the form of the m-interlacing (\(1\leq m\leq {\mathop{\rm ord}} L\), where L is a given operator) of finite sums of hypergeometric sequences, plays an important role in the Hendriks–Singer algorithm for constructing all Liouvillian solutions of L(y) = 0. We show that Hendriks–Singer’s procedure for finding solutions in the form of such m-interlacing can be simplified. We also show that the space of solutions of L(y) = 0 spanned by the solutions of the form of the m-interlacing of hypergeometric sequences possesses a cyclic permutation property. In addition, we describe adjustments of our implementation of the Hendriks–Singer algorithm to utilize the presented results.

Supported by ECONET grant 21315ZF.

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Authors and Affiliations

  1. Computing Centre of the Russian Academy of Sciences, Vavilova, 40, Moscow, 119991,GSP-1, Russia

    S. A. Abramov

  2. Institute XLIM, Université de Limoges, CNRS, 123, Av. A. Thomas, 87060, Limoges cedex, France

    M. A. Barkatou

  3. Computing Centre of the Russian Academy of Sciences, Vavilova, 40, Moscow, 119991,GSP-1, Russia

    D. E. Khmelnov

Authors
  1. S. A. Abramov
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  2. M. A. Barkatou
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  3. D. E. Khmelnov
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Editor information

Editors and Affiliations

  1. Joint Institute for Nuclear Research, Laboratory of Information Technologies, Dubna, Russia

    Vladimir P. Gerdt

  2. Technische Universität München‘, Institut für Informatik, Garching, Germany

    Ernst W. Mayr

  3. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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© 2009 Springer-Verlag Berlin Heidelberg

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Abramov, S.A., Barkatou, M.A., Khmelnov, D.E. (2009). On m-Interlacing Solutions of Linear Difference Equations. In: Gerdt, V.P., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2009. Lecture Notes in Computer Science, vol 5743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04103-7_1

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  • DOI: https://doi.org/10.1007/978-3-642-04103-7_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04102-0

  • Online ISBN: 978-3-642-04103-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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