There is a separate file for Fibonacci numbers. --------------------------------------------------------------------- 11531 Jean-Paul Allouche a.o.: Convergents of folded continued fractions. Acta Arithmetica 77 (1996), 77-96. 8298 Stephen Astels: On the sum and product of continued fractions. Internet 1996, 13p. 24190 Welleda Maria Baldoni/Carlo Ciliberto/Giulia Maria Piacentini Cattaneo: Aritmetica, crittografia, codici. Springer 2006, 520p. Eur 26. R. Ballieu: Sur le developpement des irrationelles quadratiques en fractions continues regulaires. Mathesis 54 (1942), ... Dominique Barbolosi: Fractions continues a' quotients partiels impairs. These, Univ. de Provence, Marseille 1988. Dominique Barbolosi: Sur le developpement en fractions continues a quotients partiels impairs. Monatshefte Math. 109 (1990), 25-37. 9772 Dominique Barbolosi/Hendrik Jager: On a theorem of Legendre in the theory of continued fractions. Sem. Th. Nombres Bordeaux 6 (1994), 81-94. Some refinements of Legendre's theorem on approximation coefficients. 11532 Leonard Baum/Melvin Sweet: Continued fractions of algebraic power series in characteristic 2. Ann. Math. 103 (1976), 593-610. 24871 Alan Beardon/Ian Short: A geometric representation of continued fractions. Am. Math. Monthly 121/ (2014), 391-402. 11473 M. Beeler/R. William Gosper/R. Schroeppel: Continued fractions. MIT AI Memo 239 (1972). ["Hakmem", Internet 1995.] 7947 Andreas Bender: Continued fractions against Farey fractions. Dr. Dobb's Journal May 1996, 99-101. N. Beskin: Fascinating fractions. Mir 1980. W. Beynon: A formal account of some elementary continued fraction algorithms. J. Algor. 4 (1983), 221-240. N. Blachman: The continued fraction as an information source. IEEE Trans. Inf. Theory IT-30/4 (1984), 671-674. F. Blumer: U''ber die Gu''te der Approximation einer reellen Zahl durch die Na''herungsbru''che ihrer halbregelma''s''igen Kettenbruch- entwicklungen. Comm. Math. Helv. 10 (1937), ... F. Blumer: U''ber das Wachstum der Na''herungsnenner halbregelma''s''iger Kettenbru''che. Comm. Math. Helv. 10 (1937), ... F. Blumer: U''ber die verschiedenen Kettenbruchentwicklungen beliebiger reeller Zahlen und die periodischen Kettenbruchentwicklungen quadratischer Irrationalita''ten. Acta Arithm. 3 (1938), ... 23058 Florin Boca/Joseph Vandehey: On certain statistical properties of continued fractions with even and with odd partial quotients. Internet 2012, 18p. 5820 J. Borwein/P. Borwein/D. Bailey: Ramanujan, modular equations, and approximations to Pi or how to compute one billion digits of Pi. Am. Math. Monthly 96 (1989), 201-219. Jonathan Borwein/Alf van der Poorten/Jeffrey Shallit/Wadim Zudilin: Neverending fractions. Cambridge UP 2014, 210p. Eur 35. Wieb Bosma/Hendrik Jager/F. Wiedijk: Some metrical observations on the approximation by continued fractions. Indag. Math. 45 (1983), 281-299. 24682 Wieb Bosma/Cor Kraaikamp (ed.): Continued fractions. Univ. Nijmegen 2013, 200p. C. Brezinski: History of continued fractions and Pade' approximants. Springer 1991, 550p. DM 188. 11446 Keith Brown: Integer sequences related to pi. Internet ca. 1997, 4p. 11447 Keith Brown: Continued fractions and characteristic recurrences. Internet 1997, 2p. 11616 Tom Brown: A characterization of the quadratic irrationals. Can. Math. Bull. 34 (1991), 36-41. A. Chatelet: Contribution a' la theorie des fractions continues arithmetiques. Bull. Soc. Math. France 40 (1912), ... 11615 G. Chrystal: Algebra. 2 volumes. Chelsea. 24074 John Coffey: An informal introduction to continued fractions. Internet 2011, 100p. Robert Corless/Gregory Frank/J. Graham Monroe: Chaos and continued fractions. Physica D 46 (1990), 241-253. Karma Dajani/Cor Kraaikamp: Generalization of a theorem of Kusmin. Monatshefte Math. 118 (1994), 55-73. 11510 Karma Dajani/Cor Kraaikamp: A note on the approximation by continued fractions under an extra condition. New York J. Math. 3 A (1998), 69-80. 21007 Karma Dajani/Cor Kraaikamp: Ergodic theory of numbers. MAA 2002, 190p. Eur 39. 11550 J. Les Davison: An algorithm for the continued fraction of e^{l/m}. Proc. 8th Manitoba Conf. Num. Math. Comp. 1978, 169-179. V. Detlovs: Equivalence of normal algorithms and recursive functions. Trudy Mat. Inst. Steklov 52 (1958), 75-139. 335 M. Dodson/J. Vickers (ed.): Number theory and dynamical systems. Cambridge UP 1989. 24331 W. Duke: Continued fractions and modular functions. Bull. AMS 42/2 (2005), 137-162. Gerald Edgar/Klaus Zacharias: Solution to problem E3264 - asymptotic estimates for convergents of a continued fraction. Am. Math. Monthly 97 (1990), 157. See 8450 Rabinowitz. Leonhard Euler: De fractionibus continuis. Comm. Ac. Sci. Imp. Petropol. 9 (1737), ... [Op. ser. I, vol. 14, ...] Leonhard Euler: Specimen algorithmi singularis. Novi Comm. Ac. Sci. Imp. Petropol. 9 (1762/1763), ... [Op. ser. I, vol. 15, ...] 21063 Philippe Flajolet/Brigitte Vallee: Continued fraction algorithms, functional operators, and structure constants. INRIA 1996, 35p. Wolfgang Fluch: Ein Operator der Kettenbruchtheorie. Anz. Oest. Akad. Wiss. 129 (1992), 39-49. 11505 C. Faivre: The rate of convergence of approximation of a continued fraction. J. Number Theory 68 (1998), 21-28. 14145 Francesca Guarnieri: Teoria dei numeri e sicurezza dei dati. Tesi, Ferrara 1998. S. Günther: Darstellung der Näherungswerte von Kettenbrüchen in independenter Form. Habilitationsschrift Univ. Erlangen 1872. Marshall Hall: On the sum and product of continued fractions. Annals of Mathematics 48 (1947), 966--993. 4842 J. Harrison: Geometry of algebraic continued fractals. In 335 Dodson/Vickers, 117-136. 24699 Allen Hatcher: Topology of numbers. Preliminary draft, 2013, 122p. Explains on pages 16-58 in a very nice manner and with many illustrations the connections between Farey sequences and Möbius transformations. 18273 Doug Hensley: Continued fractions. World Scientific 2006, 240p. Eur 68. 11530 Fritz Herzog: On the continued fractions of conjugate quadratic irrationalities. Can. Math. Bull. 23 (1980), 199-206. 11511 Adolf Hurwitz: U''ber die Entwicklung komplexer Gro''s''en in Kettenbru''che. Acta Math. 11 (1887/88), 187-200. 11512 Adolf Hurwitz: U''ber eine besondere Art der Kettenbruchentwicklung reeller Gro''s''en. Acta Math. 12 (1889), 367-405. 11513 Adolf Hurwitz: U''ber die angena''herte Darstellung der Irrationalzahlen durch rationale Bru''che. Math. Ann. 39 (1891), 279-284. Adolf Hurwitz: U''ber die Kettenbruchentwicklung der Zahl e. Math. Werke (1933), Band 2, 129-133. Adolf Hurwitz: U''ber die angena''herten Darstellungen der Zahlen durch rationale Bru''che. Math. Ann. 44 (1894), 417-436. 20970 Marius Iosifescu/Cor Kraaikamp: Metrical theory of continued fractions. Kluwer 2002, 380p. Eur 82. S. Ito: On Legendre's theorem related to diophantine approximations. Sem. Th. Nombres Bordeaux ... (1987/88), exp. 44, 44-01-44-19. Carl Gustav Jacobi: Allgemeine Theorie der kettenbrucha''hnlichen Algorithmen. J. reine und angew. Math. 69 (1868), 29-64. Hendrik Jager/C. Kraaikamp: On the approximation by continued fractions. Indag. Math. 51 (1989), 289-307. Hendrik Jager/P. Liardet: Distributions arithmetiques des denominateurs de convergents de fractions continues. Indag. Math. 50 (1988), 181-197. J. Jensen: Bidrag til Kaedebrokernes Teori. Festskrift til H. G. Zeuthen 1909, ... 24534 Oleg Karpenkov: Geometry of continued fractions. Springer 2013, 400p. Eur 43 (Ebook). Ott-Heinrich Keller: Eine Bemerkung zu den verschiedenen Moeglichkeiten, eine Zahl in einen Kettenbruch zu entwickeln. Math. Annalen 116 (1939), 734-741. 17736 Aleksandr Khinchin: Continued fractions. Dover 1997, 90p. Eur 7. 24551 Kyle Kneisl: The continued fraction system (and related systems). Internet 2005, 24p. G. Ko''hler: Some more predictable continued fractions. Monatshefte Math. 89 (1980), 95-100. J. Koksma: Bewijs van een stelling over kettingbreuken. Mathematica A 6 (1937), 226-231. J. Koksma: On continued fractions. Simon Stevin 29 (1951/52), 96-102. Cor Kraaikamp: A new class of continued fractions. Acta Arithm. 57 (1991), 1-39. 11555 Jeffrey Lagarias/Jeffrey Shallit: Linear fractional transformations of continued fractions with bounded partial quotients. Internet 1996, 12p. A. Legendre: Essai sur la theorie des nombres. Duprat 1798. 9771 H. Lenstra/J. Shallit: Continued fractions and linear recurrences. Math. Comp. 61 (1993), 351-354. 24738 Pierre Liardet/Pierre Stambul: Algebraic computations with continued fractions. J. Number Theory 73/1 (1998), 92-121. 26067 Gustav Lochs: Statistik der Teilnenner der zu den echten Brüchen gehörigen regelmäßigen Kettenbrüche. Monatshefte Math. 65 (1961), 27-52. 26065 Gustav Lochs: Die ersten 968 Kettenbruchnenner von \pi. Monatshefte Math. 67 (1963), 311-316. 26066 Gustav Lochs: Vergleich der Genauigkeit von Dezimalbruch und Kettenbruch. Abh. Math. Sem. Hamburg 27 (1964), 142-144. Lisa Lorentzen/Haakon Waadeland: Continued fractions with applications. North Holland 1992. J. Loxton/A. van der Poorten: Arithmetic properties of certain functions in several variables III. Bull. Austral. Math. Soc. 16 (1977), 15-47. J. Loxton/A. van der Poorten (ed.): Diophantine analysis. LN London Math. Soc. 109 (1986). 1976 Jerold Mathews: Gear trains and continued fractions. Am. Math. Monthly 97 (1990), 505-510. [3323] Keith Matthews/R. Walters: Some properties of the continued fraction expansion of m/ne^{1/q}. Proc. Camb. Phil. Soc. 67 (1970), 67-74. M. Mendes-France: Sur les fractions continues limitees. Acta Arithm. 23 (1973), 207-215. M. Mendes-France/A. van der Poorten: Some explicit continued fraction expansions. Mathematika 38 (1991), 1-9. F. Minding: U''ber das Bildungsgesetz der Za''hler und Nenner bei Verwandlung der Kettenbru''che in gewo''hnliche Bru''che. Bull. Ac. Imp. Sci. St. Petersbourg 13 (1869), ... Hermann Minkowski: ... Math. Ann. 54 (1901), 91-... Charles Moore: An introduction to continued fractions. National Council of Teachers of Math. 1964. T. Muir: The expression of a quadratic surd as a continued fraction. Glasgow 1874. T. Muir: On the phenomenon of greatest middle in the cycle of a class of periodic continued fractions. Proc. Royal Soc. Edinburgh 12 (1884), ... V. Nachreiner: Beziehungen zwischen Determinanten und Kettenbru''chen. Preisschrift Mu''nchen 1872. 8351 Morris Newman: Integral matrices. Academic Press 1973. 11504 Manash Mukherjee/Gunther Karner: Irrational numbers of constant type - a new characterization. New York J. Math. 4 (1998), 31-34. 16062 C. Olds: Continued fractions. Random House 1963, 170p. 5719 Oskar Perron: Die Lehre von den Kettenbru''chen. 2 volumes. Teubner 1954. Oskar Perron: Grundlagen fuer eine Theorie des Jacobischen Kettenbruchalgorithmus. Math. Ann. 64 (1907), 1-76. Henri Poincare': Sur une generalisation des fractions continues. CR Ac. Sci. Paris 99 (1884), 1014-1016. 11568 A. van der Poorten: An introduction to continued fractions. In Loxton/van der Poorten 1986, 99-138. 7287 A. van der Poorten: Notes on continued fractions and recurrence sequences. 7226 Loxton, 86-97. 11567 A. van der Poorten/Jeffrey Shallit: Folded continued fractions. J. Number Theory 40 (1992), 237-250. 11564 A. van der Poorten/Jeffrey Shallit: A specialised continued fraction. Can. J. Math. 45 (1993), 1067-1079. 8450 Stanley Rabinowitz: A perplexing finite continued fraction. Internet, ca. 1996, 8p. About how an explicit formula for the continued fraction [1,2,3,..,n] in terms of the n-th harmonic number 1+1/2+...+1/n was found. See also the article by Edgar/Zacharias. 18258 Gerhard Ramharter: Analysis and geometry of a gcd-algorithm. Rend. Circolo Mat. Palermo Suppl. 77 (2006), 541-552. 18259 Gerhard Ramharter: Maximal continuants and periodicity. Integers ... (2006), ... 24592 Ian Richards: Continued fractions without tears. Math. Mag. 54/4 (1981), 163-171. 19030 John Robertson/Keith Matthews: A continued fraction approach to a result of Feit. Am. Math. Monthly ... (ca. 2007), 5p. 18266 Andrew Rockett/Peter Szüsz: Continued fractions. World Scientific 1998, 180p. 24417 Tomas Sauer: Kettenbrüche. Vorl. Univ. Gießen 2005, 100p. 20961 Gertraud Schuster: Abzählungen der rationalen Zahlen und Kettenbrüche. Hausarbeit der 1. Staatsprüf. Univ. Würzburg 2006, 70p. 11533 J. Serret: Cours d'algebre superieure. 2 volumes. Gauthiers-Villars 1928. Jeffrey Shallit: Simple continued fractions for some irrational numbers I-II. J. Number Theory 11 (1979), 209-217; 14 (1982), 228-231. 11503 Jeffrey Shallit: Real numbers with bounded partial quotients - a survey. L'Ens. Math. 38 (1992), 151-187. H. Siebeck: U''ber periodische Kettenbru''che. J. reine u. angew. Math. 33 (1846), ... 22991 Martin Solte: Kettenbrüche. Proseminarvortrag Univ. Heidelberg 2009, 18p. 24651 Pierre Stambul: Continued fractions with bounded partial quotients. Proc. AMS 128/4 (1999), 981-985. 11613 Harold Stark: An introduction to number theory. MIT Press 1987, 340p. Eur 33. M. Stern: Theorie der Kettenbrüche und ihre Anwendung. J. reine u. angew. Math. 10 (1832), ..., 11 (1832), ... M. Stern: Zur Theorie der periodischen Kettenbrüche. J. reine u. angew. Math. 53 (1857), ... R. Steuerwald: U''ber die Perioden regelma''s''iger Kettenbru''che fu''r Quadratwurzeln aus ganzen Zahlen. Math. Zeit. 52 (1950), ... 23022 Philipp Stopp: Zur Arithmetik von Kettenbrüchen. DA Univ. Saarbrücken 2009, 110p. James Joseph Sylvester: On a remarkable modification of Sturm's theorem. London Edinburgh Dublin Philos. Mag. J. Sci. 5 (1853), ... 19287 Godfried Toussaint: The euclidean algorithm generates traditional musical rhythms. Internet 2006, 25p. 23102 Ilan Vardi: Continued fractions from Euclid to the present day. Internet 2009, 41p. 24256 Linas Vepstas: Continued fractions and gaps. Internet 2004, 29p. 18243 Linas Vepstas: The Gauss-Kuzmin-Wirsing operator. Internet 2005, 21p. 18244 Linas Vepstas: A series representation for the Riemann zeta function derived from the Gauss-Kuzmin-Wirsing operator. Internet 2005, 18p. 18246 Linas Vepstas: Symmetries of period doubling maps. Internet 2006, 54p. 16635 Carlo Viola: Approssimazione diofantea, frazioni continue e misure d'irrazionalita'. Boll. UMI Mat. Soc. Cultura Agosto 2004, 291-320. G. Voronoi: On a generalization of the algorithm for continued fractions. Dissertation, Warsaw 1896. Russian. 11443 H. Wall: Analytic theory of continued fractions. Van Nostrand 1948. 24333 R. Walters: Alternate derivation of some regular continued fractions. J. Austral. Math. Soc. 8 (1968), 205-212. Clever use of matrices is made to derive a new proof of the expansion of e^(1/q) and e^(2/q). R. Walters: Number theory. An introduction. Carslaw, Sydney 1987. 0-9589105-6-1. 11468 Eric Weisstein: Continued fraction constant. Internet 1998, 2p. 11469 Eric Weisstein: Continued fraction. Internet 1998, 10p. 11472 Eric Weisstein: Continued fraction constants. Internet 1998, 6p. Hugh Williams: A numerical investigation into the length of the period of the continued fraction expansion of \sqrt(D). Math. Comp. 36 (1981), 593-601. Hugh Williams: Continued fractions and number-theoretic computations. Rocky Mount. J. Math. 15 (1985), 621-655. E. Wo''lffing: Wer hat u''ber Kettenbru''che gearbeitet? Math.-naturwiss. Mitt. 10 (1908), ... An extensive bibliography.