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Continued Fractions and Padé Approximation Method

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Classical and New Inequalities in Analysis

Part of the book series: Mathematics and Its Applications () ((MAEE,volume 61))

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Abstract

The modern theory of (infinite) continued fractions probably begins with Bombelli (1526–1672) [1] in which he computes the square roots of numbers by the following device.

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References

  1. BOMBELLI, R., “L’Algebra Opera”, Bologna, 1579.

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  2. BREZINSKI, C., The long history of continued fractions and Padé approximants, “Padé Approximation and its Applications Amsterdam 1980”, Lecture Notes 888, Berlin, Heidelberg, New York, 1981.

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  3. JONES, W. B. and W. J. THRON, “Continued Fractions, Analytic Theory and Applications”, Reading, 1980.

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  4. BREZINSKI, C., “History of Continued Fractions and Padé Approximants”, Berlin, New York, 1991.

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  5. PADE, H., Sur la représentation approchée d’une fonction pour des fractions rationnelles,Ann. Sci. École Norm. Sup. Suppl. [3] 9 (1892), 1–93. (Thesis)

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  6. BOWMAN, K. O. and L. R. SHELTON, “Continued Fractions in Statistical Applications”, New York, Basel, 1989.

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  7. BAKER, G. A., Jr., “Essentials of Padé Approximants”, New York, San Francisco, London, 1975.

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  8. GILEWICZ, J. and A. P. MAGNUS, Sharp inequalities for the Padé approximant errors in the Stieltjes case,Rocky Math. J. 21 (1991), 227233.

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© 1993 Springer Science+Business Media Dordrecht

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Mitrinović, D.S., Pečarić, J.E., Fink, A.M. (1993). Continued Fractions and Padé Approximation Method. In: Classical and New Inequalities in Analysis. Mathematics and Its Applications (East European Series), vol 61. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1043-5_25

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  • DOI: https://doi.org/10.1007/978-94-017-1043-5_25

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4225-5

  • Online ISBN: 978-94-017-1043-5

  • eBook Packages: Springer Book Archive

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