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δ-Fraction expansions of analytic functions

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References

  1. D. Dijkstra, A continued fraction expansion for a generalization of Dawson’s Integral, Math. of Comp. 31 (1977), 503–510.

    MathSciNet  MATH  Google Scholar 

  2. D. M. Drew and J. A. Murphy, Branch points, M-fractions, and rational approximants generated by linear equations, J. Inst. Maths. Applics. 19 (1977), 169–185.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. V.K. Dzjadyk, On the asymptotics of diagonal Padé approximants of the functions sin z, cos z, sinh z, and cosh z. Math. USSR Sbornik 36 (1980), 231–249.

    CrossRef  MATH  Google Scholar 

  4. J.S. Frame, The Hankel power sum matrix inverse and the Bernoulli continued fraction, Math. of Comp. 33 (1979), 815–816.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. A.O. Gel’fond, Calculus of Finite Differences (Authorized English translation of the third Russian edition) Hinustan Publishing Corporation (India), 1971.

    MATH  Google Scholar 

  6. J. Gill, Enhancing the convergence region of a sequence of bilinear transformations, Math. Scand. 43 (1978), 74–80.

    MathSciNet  MATH  Google Scholar 

  7. -, The use of attractive fixed points in acclerating the convergence of limit-periodic continued fractions, Proc. Amer. Math. Soc. 47 (1975), 119–126.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. T.L. Hayden, Continued fraction approximation to functions, Numer. Math. 7 (1965), 292–309.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. W.B. Jones and W.J. Thron, Continued Fractions: Analytic Theory and Applications, Encyclopedia of Mathematics and Its Applications, Vol. 11, Addison-Wesley, Reading, Massachusetts, 1980.

    MATH  Google Scholar 

  10. W.B. Jones and W.J. Thron, Sequences of meromorphic functions corresponding to a formal Laurent series, Siam J. Math. Anal. 10 (1979), 1–17.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. S.S. Khloponin, Approximation of functions by continued fractions, Izvestiya VUZ. Matematika 23 (1979), 37–41.

    MathSciNet  MATH  Google Scholar 

  12. A.N. Khovanskii, The Applications of Continued Fractions and Their Generalizations to Problems in Approximation Theory, English translation by Peter Wynn, Noordhoff, 1963.

    Google Scholar 

  13. W. Leighton and W.T. Scott, A general continued fraction expansion, Bull. Amer. Math. Soc., (1939), 596–605.

    Google Scholar 

  14. A. Magnus, Certain continued fractions associated with the Padé table, Math. Zeitschr. 78 (1962), 361–374.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. A. Magnus, Expansion of power series into P-fractions, Math. Zeitschr. 80 (1962), 209–216.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. J.H. McCabe, A continued fraction expansion, with a truncation error estimate, for Dawson’s integral, Math. of Comp. 28 (1974), 811–816.

    MathSciNet  MATH  Google Scholar 

  17. J.H. McCabe, A further correspondence property of M-fractions, Math. of Comp. 32 (1978), 1303–1305.

    MathSciNet  MATH  Google Scholar 

  18. J.H. McCabe and J.A. Murphy, Continued fractions which correspond to power series expansions at two points, J. Inst. Maths. Applics. 17 (1976), 233–247.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. L.M. Milne-Thomson, The Calculus of Finite Differences MacMillan and Co., London, 1933, Chapter XVII.

    MATH  Google Scholar 

  20. J.A. Murphy, Certain rational function approximations to (1+x2)−1/2, J. Inst. Maths. Applics. 7 (1971), 138–150.

    CrossRef  MATH  Google Scholar 

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

    MATH  Google Scholar 

  22. -, Über die Poincarésche lineare Differenzengleichung, J. Reine Angew. Math. 137 (1909), 6–64.

    MathSciNet  MATH  Google Scholar 

  23. -, Über einen Satz des Herrn Poincaré, J. Reine Angew. Math. 136 (1909), 17–37.

    MathSciNet  MATH  Google Scholar 

  24. -, Über Summengleichungen und Poincarésche Differenzengleichungen, Math. Ann. 84 (1921), 1–15.

    CrossRef  MathSciNet  MATH  Google Scholar 

  25. H. Poincaré, Sur les Equations Linéaires aux Différentielles ordinaires et aux Différences finies, Amer. J. Math., VIII (1885), 203–258.

    CrossRef  MATH  Google Scholar 

  26. W.J. Thron, Some properties of continued fractions 1+d0z+K(z/(1+dn(z)), Bull. Amer. Math. Soc. 54 (1948), 206–218.

    CrossRef  MathSciNet  MATH  Google Scholar 

  27. W.J. Thron and H. Waadeland, Accelerating convergence of limit periodic continued fractions K(an/1), Numer. Math. 34 (1980), 155–170.

    CrossRef  MathSciNet  MATH  Google Scholar 

  28. -, Analytic continuation of functions defined by means of continued fractions, Math. Scand. 47 (1980), 72–90.

    MathSciNet  MATH  Google Scholar 

  29. W.J. Thron and H. Waadeland, Convergence questions for limit periodic continued fractions, Rocky Mountain J. Math. (1981).

    Google Scholar 

  30. H.B. Van Vleck, On the convergence of algebraic continued fractions, whose coefficients have limiting values, Trans. Amer. Math. Soc. 5 (1904), 253–262.

    CrossRef  MathSciNet  MATH  Google Scholar 

  31. H. Waadeland, General T-fractions corresponding to functins satisfying certain boundedness conditions, J. Approx. Theory, 26 (1979), 317–328.

    CrossRef  MathSciNet  MATH  Google Scholar 

  32. H. Waadeland, Limit periodic general T-fractions and holomorphic functions, J. Approx. Theory 27 (1979), 329–345.

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

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© 1982 Springer-Verlag

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Lange, L.J. (1982). δ-Fraction expansions of analytic functions. In: Jones, W.B., Thron, W.J., Waadeland, H. (eds) Analytic Theory of Continued Fractions. Lecture Notes in Mathematics, vol 932. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0093312

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  • DOI: https://doi.org/10.1007/BFb0093312

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