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Orthogonal polynomials, chain sequences, three-term recurrence relations and continued fractions

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Computational Methods and Function Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1435))

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References

  1. A. Auric, Recherches sur les fractions continues algébraiques, J. Math. Pures Appl. (6) 3 (1907).

    Google Scholar 

  2. T. S. Chihara, Introduction to Orthogonal Polynomials, Mathematics and Its Applications Ser., Gordon, 1978.

    MATH  Google Scholar 

  3. L. Jacobsen, Composition of linear fractional transformations in terms of tail sequences, Proc. Amer. Math. Soc. (1) 97 (1986), 97–104.

    Article  MathSciNet  MATH  Google Scholar 

  4. L. Jacobsen and W. J. Thron, Oval convergence regions and circular limit regions for continued fractions K(a n/1), Lecture Notes in Math., Springer-Verlag 1199 (1986), 90–126.

    Article  MathSciNet  MATH  Google Scholar 

  5. W.B. Jones, W. J. Thron, Convergence of continued fractions, Canad. J. Math. 20 (1968), 1037–1055.

    Article  MathSciNet  MATH  Google Scholar 

  6. W.B. Jones, W.J. Thron, Continued Fractions. Analytic Theory and Applications. Encyclopedia of mathematics and its applications, 11, Addison-Wesley, 1980.

    Google Scholar 

  7. R.E. Lane, The convergence and values of periodic continued fractions, Bull. Amer. Math. Soc. 51 (1945), 246–250.

    Article  MathSciNet  MATH  Google Scholar 

  8. O. Perron, Die Lehre von den Kettenbrüchen, Band II, Teubner, Stuttgart, 1957.

    MATH  Google Scholar 

  9. S. Pincherle, Delle funzioni ipergeometriche e di vari questioni ad esse attinenti, Giorn. Mat. Battaglini 32 (1894), 209–291.

    Google Scholar 

  10. W.T. Scott, H.S. Wall, A convergence theorem for continued fractions, Trans. Amer. Math. Soc 47 (1940), 155–172.

    Article  MathSciNet  MATH  Google Scholar 

  11. H. Waadeland, Tales about tails, Proc. Amer. Soc. (1) 90 (1984), 57–64.

    Article  MathSciNet  MATH  Google Scholar 

  12. H.S. Wall, Analytic Theory of Continued Fractions, Van Nostrand, New York, 1948.

    MATH  Google Scholar 

  13. J.D. Worpitzky, Untersuchungen über die Entwicklung der monodromen und monogenen Funktionen durch Kettenbrüche, Friedrichs-Gymnasium und Realschule, Berlin, Jahresbericht 1865, 3–39.

    Google Scholar 

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Authors and Affiliations

  1. Division of Mathematical Sciences, The University of Trondheim, N-7034, Trondheim, Norway

    Lisa Jacobsen

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  1. Lisa Jacobsen
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Stephan Ruscheweyh Edward B. Saff Luis C. Salinas Richard S. Varga

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© 1990 Springer-Verlag

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Jacobsen, L. (1990). Orthogonal polynomials, chain sequences, three-term recurrence relations and continued fractions. In: Ruscheweyh, S., Saff, E.B., Salinas, L.C., Varga, R.S. (eds) Computational Methods and Function Theory. Lecture Notes in Mathematics, vol 1435. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087900

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  • DOI: https://doi.org/10.1007/BFb0087900

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52768-8

  • Online ISBN: 978-3-540-47139-4

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