On the Convergence of Limit Periodic Continued Fractions K (an/1) where an ... 1/4. Part IV

Lorentzen, Lisa
January 2002
Constructive Approximation;2002, Vol. 18 Issue 1, p1
Academic Journal
Continued fractions K (a[SUBn]/B[SUBn]), where a[SUBn], b[SUBn] &epsis; C and a[SUBn]/b[SUBn]b[SUBn-1] ? -� may converge or diverge depending on how a[SUBn]/b[SUBn]b[SUBn-1] approaches its limit. Due to equivalence transformations it suffices to study the special case where all b[SUBn] = 1. We shall prove that K (a[SUBn]/1) converges if a[SUBn] ? -� and there exists a set V ? C ? {8} with certain properties such that a[SUBn]/(1 + V) ? V for all n. We shall also summarize some other useful consequences of such value sets V.


Related Articles

  • A note on the l�vy constant for continued fractions. Ting Zhong // Turkish Journal of Mathematics;2009, Vol. 33 Issue 4, p315 

    In this note, we study the l�vy constant of continued fraction expansions. We show that for all x ? [0, 1), the upper l�vy constant of x is finite except a set with Hausdorff dimension one-half.

  • An approach to renormalization on the n-torus. Rockmore, Daniel; Siegel, Ralph; Tongring, Nils; Tresser, Charles // Chaos;Jul91, Vol. 1 Issue 1, p25 

    Discusses the coding theory of rotations and the continued fractions algorithm. Rotations' relation to flows; Even two-coloring of integers with a given proportion; Definition of n-coloring of the integers; Coding of rotations on a certain torus by considering linear flows on the n-torus;...

  • Book reviews. Niven, Ivan // Bulletin (New Series) of the American Mathematical Society;Jan1994, Vol. 30 Issue 1, p109 

    Reviews the book, `Continued Fractions,' by Andrew M. Rockett and Peter Szusz.

  • Appendix C. Rotations, Continued Fractions, and Rational Approximation. Milnor, John // Dynamics in One Complex Variable;2006, p234 

    A discussion on rotations, continued fractions and rotational approximation that appeared in the book "Dynamics in One Complex Variable," third edition, by John Milnor is presented.

  • Continuing the fraction. Lubinksy, D.S. // South African Journal of Science;Aug96, Vol. 92 Issue 8, p363 

    Discusses the mathematical process of division and the notion of continued fractions. Association between approximation of `pi' and the development of continued fraction; Usefulness in representation and computation of functions; Problem of `spurious poles' in functions.

  • Continued fraction analysis of the duration of an... Guillemin, Fabrice; Pinchon, Didier // Journal of Applied Probability;Mar1998, Vol. 35 Issue 1, p165 

    Presents a study which shows how the Laplace transforms theta of the duration of an excursion by the occupation process. Representation of theta by a continued fraction; Distribution of a congestion duration; Results of the study.

  • QD-Type Algorithms for the Nonnormal Newton-Padé Approximation Table. Beckermann, B.; Carstensen, C. // Constructive Approximation;1996, Vol. 12 Issue 3, p307 

    It is well known that solutions of the rational interpolation problem or Newton -- Padé approximation problem can be represented with the help of continued fractions if certain normality assumptions are satisfied. By comparing two interpolating continued fractions, one obtains a recursive...

  • THE LIMITING CASE OF THIELE'S INTERPOLATING CONTINUED FRACTION EXPANSION. Jie-qing Tan // Journal of Computational Mathematics;Jul2001, Vol. 19 Issue 4, p433 

    Analyzes the limiting case of Thiele's interpolating continued fraction expansion which is established in terms of inverse differences. Method used for the analysis; Example of showing that the limiting Thiele's continued fraction expansion can be determined once for all instead of carrying out...

  • Continued Nested Radical Fractions. TEIK-CHENG LIM // Mathematical Spectrum;2009/2010, Vol. 42 Issue 2, p59 

    The article discusses nested radicals (NR) and continued fractions (CF) in the form of golden ratio, silver ratio and plastic content. Continued nested radical fractions (CNRF) is defined as a hybrid of a CF and a NR. The author says that NR and CF are considered as special cases of CNRF. It is...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics