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Continued fractions with restricted variation properties

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Summary

Conditions are studied under which a continued fraction has the property that for each positive integer k, its sequence of approximants is a finite linear combination of convergent sequences having nonnegative k-th differences.

References

  1. [1]

    D. F. Dawson,Continued fractions with absolutely convergent even or odd part, Canadian J. Math.,11 (1959), pp. 131–140.

  2. [2]

    D. F. Dawson,Mapping properties of matrix summability methods, Annali Mat. Pura Appl., (4),88 (1971), pp. 1–8.

  3. [3]

    D. F. Dawson,Matrix methods which sum sequences of bounded k-variation, Pub. Inst. Math. (Beograd),12 (1971), pp. 37–40.

  4. [4]

    D. F. Dawson,Remarks on some convergence conditions for continued fractions, Proc. Amer. Math. Soc.,18 (1967), pp. 803–805.

  5. [5]

    D. F. Dawson,Variation properties of sequences, Mat. Vesnik,6 (1969), pp. 437–441.

  6. [6]

    J. Farinha,Sur la convergence de φa i /l, Portugal Math.,13 (1954), pp. 145–148.

  7. [7]

    R. E. Lane -H. S. Wall,Continued fractions with absolutely convergent even and odd parts, Trans. Amer. Math. Soc.,67 (1949), pp. 368–380.

  8. [8]

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

  9. [9]

    W. J. Thron,Zwillingskonvergenzgebiete für Kettenbruche 1 +K(a n /l) deren eines die Kreisscheibe |a 2n−1 |<ϱ 2 ist, Math. Zeit.,70 (1959), pp. 310–344.

  10. [10]

    H. S. Wall,Analytic theory of continued fractions, New York, 1948.

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Dedicated to the memory of ProfessorH. S. Wall

Entrata in Redazione l’8 giugno 1974.

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Dawson, D.F. Continued fractions with restricted variation properties. Annali di Matematica 106, 219–231 (1975). https://doi.org/10.1007/BF02415030

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Keywords

  • Positive Integer
  • Linear Combination
  • Continue Fraction
  • Variation Property
  • Convergent Sequence