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Connection Problem for Regular Holonomic Systems in Several Variables

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Analytic, Algebraic and Geometric Aspects of Differential Equations

Part of the book series: Trends in Mathematics ((TM))

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Abstract

We formulate the connection problem for regular holonomic systems in several variables on the basis of local monodromies. As examples, we solve the connection problem for Appell’s hypergeometric functions F 1 and F 2.

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Acknowledgements

This work is supported by the JSPS grants-in-aid for scientific research B, No. 15H03628.

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Authors and Affiliations

  1. Department of Mathematics, Kumamoto University, Kumamoto, 860-8555, Japan

    Yoshishige Haraoka

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  1. Yoshishige Haraoka
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Correspondence to Yoshishige Haraoka .

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Editors and Affiliations

  1. Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Warsaw, Poland

    Galina Filipuk

  2. Kumamoto University, Kumamoto, Japan

    Yoshishige Haraoka

  3. Faculty of Mathematics and Natural Sciences, Cardinal Stefan Wyszynski University, Warsaw, Poland

    Sławomir Michalik

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Haraoka, Y. (2017). Connection Problem for Regular Holonomic Systems in Several Variables. In: Filipuk, G., Haraoka, Y., Michalik, S. (eds) Analytic, Algebraic and Geometric Aspects of Differential Equations. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-52842-7_8

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