The geometry of Pringsheim's continued fractions

被引：6
|
作者：
Beardon, AF [1 ]
机构：
[1] Univ Cambridge, Ctr Math Sci, Dept Pure Math & Math Stat, Cambridge CB30 WB, England
来源：
GEOMETRIAE DEDICATA | 2001年 / 84卷 / 1-3期
关键词：
continued fractions; Pringsheim; inverse points;
D O I：
10.1023/A:1010361030641
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give a completely geometric interpretation of Pringsheim's classical convergence criterion for continued fractions, and we use this to derive the convergence of, and other information about, the continued fraction.
引用
收藏
页码：125 / 134
页数：10
相关论文
共 50 条
  • [41] On The Convergent of θ-Expansions of Continued Fractions
    Muhammad, Khairun Nisak
    Kamarulhaili, Hailiza
    PROCEEDING OF THE 25TH NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES (SKSM25): MATHEMATICAL SCIENCES AS THE CORE OF INTELLECTUAL EXCELLENCE, 2018, 1974
  • [42] Continued fractions and Hardy sums
    Lageler, Alessandro
    ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG, 2024, 94 (02): : 107 - 128
  • [43] Continued fractions and Stern polynomials
    Karl Dilcher
    Larry Ericksen
    The Ramanujan Journal, 2018, 45 : 659 - 681
  • [44] GENERALIZED PALINDROMIC CONTINUED FRACTIONS
    Freeman, David M.
    ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2018, 48 (01) : 219 - 236
  • [45] Continued fractions and transcendental numbers
    Adamczewski, Boris
    Bugeaud, Yann
    Davison, Les
    ANNALES DE L INSTITUT FOURIER, 2006, 56 (07) : 2093 - 2113
  • [46] Rotation algebras and continued fractions
    Boca, Florin P.
    OPERATOR ALGEBRAS, OPERATOR THEORY AND APPLICATIONS, 2008, 181 : 121 - 142
  • [47] Difference equations and continued fractions
    Trigiante, Donato
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 69 (03) : 1057 - 1066
  • [48] The Parabola Theorem on Continued Fractions
    Short, Ian
    COMPUTATIONAL METHODS AND FUNCTION THEORY, 2016, 16 (04) : 653 - 675
  • [49] GOOD APPROXIMATIONS AND CONTINUED FRACTIONS
    KRAAIKAMP, C
    LIARDET, P
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 112 (02) : 303 - 309
  • [50] SOME CONTINUED FRACTIONS FOR π AND G
    Nimbran, Amrik Singh
    Levrie, Paul
    INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2017, 48 (02): : 187 - 204
12345