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Order stars and the structure of Padé tableaux

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Padé Approximation and its Applications Bad Honnef 1983

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1071))

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Abstract

We demonstrate by using the theory of order stars that analytic properties of complex functions impose bounds on the maximal block size in their Padé tableau. After a short survey of the relevant parts of order star theory we sketch the proofs of three theorems that provide realistic upper bounds on the block size in terms of zeros and essential singularities of the underlying function. These theorems are applied to investigate the structure of Padé tableaux of Jν, the Bessel function, and Eα, the Mittag-Leffler function.

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References

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Authors and Affiliations

  1. King’s College, University of Cambridge, CB2 1ST, Cambridge, England

    A. Iserles

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  1. A. Iserles
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Helmut Werner Hans Josef Bünger

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© 1984 Springer-Verlag

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Iserles, A. (1984). Order stars and the structure of Padé tableaux. In: Werner, H., Bünger, H.J. (eds) Padé Approximation and its Applications Bad Honnef 1983. Lecture Notes in Mathematics, vol 1071. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099617

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  • DOI: https://doi.org/10.1007/BFb0099617

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13364-3

  • Online ISBN: 978-3-540-38914-9

  • eBook Packages: Springer Book Archive

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