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Neverending Fractions
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[1] B., Adamczewski and Y., Bugeaud, On the Maillet-Baker continued fractions, J. Reine Angew. Math. 606 (2007), 105–121.
[2] W. W., Adams and J. L., Davison, A remarkable class of continued fractions, Proc. Amer. Math. Soc. 65 (1977), 194–198.
[3] W. W., Adams and M. J., Razar, Multiples of points on elliptic curves and continued fractions, Proc. London Math. Soc. 41 (1980), 481–498.
[4] G., Almkvist and W., Zudilin, Differential equations, mirror maps and zeta values, in: Mirror symmetry y, AMS/IP Stud. Adv. Math. 38 (Amer. Math. Soc., Providence, RI, 2006), pp. 481–515.
[5] G., Andrews and B. C., Berndt, Ramanujan's lost notebook, Parts I, II, II, IV (Springer, New York, 2005, 2009, 2012, 2013).
[6] G. E., Andrews, B. C., Berndt, L., Jacobsen and R. L., Lamphere, The continued fractions found in the unorganized portions of Ramanujan's notebooks, Mem. Amer. Math. Soc. 99 (Amer. Math. Soc., Providence, RI, 1992), no. 477.
[7] F., Apéry, Roger Apéry, 1916-1994: a radical mathematician, Math. Intelligencer 18 (1996), no. 2, 54–61.
[8] R., Apéry, Irrationalité de ζ(2) et ζ(3), Journées arithmétiques de Luminy (20-24 June 1978), Asterisque 61 (Soc. Math.France, Paris, 1979), 11–13.
[9] D. H., Bailey, J. M., Borwein and R. H., Crandall, On the Khintchine constant, Math. Comp. 66 (1997), 417–431.
[10] A., Baker, A concise introduction to the theory of numbers (Cambridge University Press, Cambridge, 1984).
[11] J., Barát and P. P., Varjú, Partitioning the positive integers to seven Beatty sequences, Indag. Math. (NS) 14 (2003), 149–161.
[12] A. F., Beardon and I., Short, The Seidel, Stern, Stolz and Van Vleck theorems on continued fractions, Bull. London Math. Soc. 42 (2010), 457–466.
[13] B. C., Berndt, Ramanujan's notebooks, Parts I, II, III, IV, V (Springer-Verlag, New York, 1985, 1989, 1991, 1994, 1998).
[14] T. G., Berry, On periodicity of continued fractions in hyperelliptic function fields, Arch. Math. (Basel) 55 (1990), 259–266.
[15] M. R., Best and H. J. J., te Riele, On a conjecture of Erdős concerning sums of powers of integers, Report NW 23/76 (Mathematisch Centrum Amsterdam, 1976).
[16] F., Beukers, A note on the irrationality of ζ(2) and ζ(3), Bull. London Math. Soc. 11 (1979), 268–272.
[17] P. E., Böhmer, Über die Transzendenz gewisser dyadischer Brüche, Math. Ann. 96 (1927), 367–377; Erratum, Math. Ann. 96 (1927), 735.
[18] E., Bombieri and A. J., van der Poorten, Continued fractions of algebraic numbers, in: Computational algebra and number theory, Sydney, 1992, Math. Appl. 325 (Kluwer, Dordrecht, 1995), pp. 137–152.
[19] D., Borwein, J., Borwein, R., Crandall and R., Mayer, On the dynamics of certain recurrence relations, Ramanujan J. 13 (2007), 63–101.
[20] D., Borwein, J. M., Borwein and B., Sims, On the solution of linear mean recurrences, Amer. Math. Monthly (2014), in press.
[21] J., Borwein and D., Bailey, Mathematics by experiment. Plausible reasoning in the 21st century, 2nd edition (A. K. Peters, Wellesley, MA, 2008).
[22] J. M., Borwein, D., Bailey and R., Girgensohn, Experimentation in mathematics: computational paths to discovery (A. K. Peters, Natick, MA, 2004).
[23] J., Borwein and P., Borwein, On the generating function of the integer part: [na + γ], J. Number Theory 43 (1993), no. 3, 293–318.
[24] J., Borwein, P., Borwein and K., Dilcher, Pi, Euler numbers and asymptotic expansions, Amer. Math. Monthly 96 (1989), 681–687.
[25] J. M., Borwein, K.-K. S., Choi and W., Pigulla, Continued fractions of tails of hypergeometric series, Amer. Math. Monthly 112 (2005), 493–501.
[26] J., Borwein, R., Crandall and G., Fee, On the Ramanujan AGM fraction. Part I: the real-parameter case, Exp. Math. 13 (2004), 275–286.
[27] J., Borwein and R., Crandall, On the Ramanujan AGM fraction. Part I: the complex-parameter case, Exp. Math. 13 (2004), 287–296.
[28] J. M., Borwein and P., Borwein, Pi and the AGM: a study in analytic number theory and computational complexity (John Wiley, New York, 1987).
[29] J., Borwein and R., Luke, Dynamics of a Ramanujan-type continued fraction with cyclic coefficients, Ramanujan J. 16 (2008), 285–304.
[30] J., Borwein and R., Luke, Dynamics of some random continued fractions, Abstract Appl. Anal. 5 (2005), 449–468.
[31] J. M., Borwein, I., Shparlinski and W., Zudilin (eds.), Number theory and related fields: in memory of Alf van der Poorten, Springer Proc. Math. and Stat. 43 (Springer-Verlag, New York, 2013).
[32] P., Borwein, S., Choi, B., Rooney and A., Weirathmueller, The Riemann hypothesis: a resource for the afficionado and virtuoso alike, CMS Books in Math. (Springer-Verlag, New York, 2007).
[33] J., Bourgain and A., Kontorovich, On Zaremba's conjecture, CR Math. Acad. Sci. Paris Ser. I Math. 349 (2011), 493–495.
[34] D., Bowman, A new generalization of Davison's theorem, Fibonacci Quart. 26 (1988), 40–45.
[35] R. P., Brent, A. J., van der Poorten and H. TE, Riele, A comparative study of algorithms for computing continued fractions of algebraic numbers, in: Algorithmic number theory (Talence, 1996), Lecture Notes in Computer Sci. 1122 (Springer, Berlin, 1996), pp. 35–47.
[36] E. B., Burger, Exploring the number jungle: a journey into Diophantine analysis, Student Math. Library 8 (Amer. Math. Soc., Providence, RI, 2000).
[37] E. B., Burger and T., Struppeck, On frequency distributions of partial quotients of U-numbers, Mathematika 40 (1993), 215–225.
[38] W., Butske, L. M., Jaje and D. R., Mayernik, On the equation, pseudoperfect numbers, and perfectly weighted graphs, Math. Comp. 69 (2000), 407–420.
[39] G., Cairns, N. B., Ho and T., Lengyel, The Sprague-Gundy function of the real game Euclid, Discrete Math. 311 (2011), 457–462.
[40] D. G., Cantor, Computing in the Jacobian of a hyperelliptic curve, Math. Comp. 48 (1987), no. 177, 95–101.
[41] D. G., Cantor, On the analogue of the division polynomials for hyperelliptic curves, J. fur Math. (Crelle) 447 (1994), 91–145.
[42] D. G., Cantor, P. H., Galyean and H. G., Zimmer, A continued fraction algorithm for real algebraic numbers, Math. Comp. 26 (1972), 785–791.
[43] J. W. S., Cassels, An introduction to Diophantine approximation, Cambridge Tracts in Math. and Math. Phys. 45 (Cambridge University Press, New York, 1957).
[44] B. M., Char, On Stieltjes' continued fraction for the gamma function, Math. Comp. 34 (1980), 547–551.
[45] S. D., Chowla, Some problems of diophantine approximation (I), Math. Z. 33 (1931), 544–563.
[46] F. W., Clarke, W. N., Everitt, L. L., Littlejohn and S. J. R., Vorster, H. J. S., Smith and the Fermat two squares theorem, Amer. Math. Monthly 106 (1999), 652–665.
[47] H., Cohn, A short proof of the simple continued fraction expansion of e, Amer. Math. Monthly 113 (2006), 57–62.
[48] R. M., Corless, G. W., Frank and J. G., Monroe, Chaos and continued fractions, Phys. D 46 (1990), 241–253.
[49] T. W., Cusick and M. Mendes, France, The Lagrange spectrum of a set, Acta Arith. 34 (1979), 287–293.
[50] A., Cuyt, V. B., Petersen, B., Verdonk, H., Waadeland and W. B., Jones, Handbook of continued fractions for special functions, with contributions by F., Backeljauw and C., Bonan-Hamada (Springer, New York, 2008).
[51] D. P., Dalzell, On 22/7, J. London Math. Soc. 19 (1944), 133–134.
[52] L. V., Danilov, Some classes of transcendental numbers, Mat. Zametki 12 (1972), 149–154; English translation, Math. Notes Acad. Sci. USSR 12 (1972), 524-527.
[53] H., Davenport, A note on diophantine approximation (II), Mathematika 11 (1964), 50–58.
[54] C. S., Davis, A note on rational approximation, Bull. Austral. Math. Soc. 20 (1979), no. 3, 407–410.
[55] J. L., Davison, A series and its associated continued fraction, Proc. Amer. Math. Soc. 63 (1977), 29–32.
[56] J. L., Davison and J. O., Shallit, Continued fractions for some alternating series, Monat shefte Math. 111 (1991), 119–126.
[57] P., Erdős, Advanced problem 4347, Amer. Math. Monthly 56 (1949), 343.
[58] S. R., Finch, Mathematical constants, Encyclopedia of Math. and its Applications 94 (Cambridge University Press, Cambridge, 2003).
[59] S., Fomin and A., Zelevinsky, The Laurent phenomenon, Adv. Appl. Math. 28 (2002), 119–144.
[60] L. R., Ford, Fractions, Amer. Math. Monthly 45 (1938), 586–601.
[61] A. S., Fraenkel, The bracket function and complementary sets of integers, Adv. Appl. Math. 28 (2002), 119–144.
[62] A. S., Fraenkel, Complementing and exactly covering sequences, J. Combin. Theory Ser. A 14 (1973), 8–20.
[63] J. S., Frame, Continued fractions and matrices, Amer. Math. Monthly 56 (1949), 98–103.
[64] J., Franel, Les suites de Farey et le problème des nombres premiers, Göttinger Nachrichten (1924), 198–201.
[65] Y., Gallot, P., Moree, and W., Zudilin, The Erdős–Moser equation 1k + 2k + … + (m - 1)k = mk revisited using continued fractions, Math. Comp. 80 (2011), no. 274, 1221–1237.
[66] A. O., Gelfond, Calculus of finite differences, International Monographs on Advanced Math. and Phys. (Hindustan Publishing, Delhi, 1971).
[67] R. L., Graham, Covering the positive integers by disjoint sets of the form {[nα + β]: n = 1, 2,…}, J. Combin. Theory Ser. A 15 (1973), 354–358.
[68] R. L., Graham, D. E., Knuth and O., Patashnik, Concrete mathematics (Addison-Wesley, Reading, MA, 1990).
[69] D. B., Grünberg and P., Moree, Sequences of enumerative geometry: congruences and asymptotics. With an appendix by Don Zagier, Exp. Math. 17 (2008), 409–426.
[70] R. K., Guy, Unsolved problems in number theory, 3rd edition, Problem Books in Math. (Springer, New York, 2004).
[71] D., Hanson, On the product of the primes, Can. Math. Bull. 15 (1972), 33–37.
[72] G. H., Hardy and E. M., Wright, An introduction to the theory of numbers, 5th edition (Oxford University Press, Oxford, 1989).
[73] H. A., Helfgott, Major arcs for Goldbach's theorem, Preprint arXiv: 1305.2897v2 [math. NT] (June 2013).
[74] M., Hirschhorn, Lord Brouncker's continued fraction for π, Math. Gazette 95 (2011), no. 533, 322–326.
[75] A. N. W., Hone, Elliptic curves and quadratic recurrence sequences, Bull. London Math. Soc. 37 (2005), 161–171.
[76] A., Hurwitz and N., Kritikos, Lectures on number theory (Springer-Verlag, Berlin, 1986).
[77] A. E., Ingham, The distribution of prime numbers, Reprint of the 1932 original, with a foreword by R. C., Vaughan, Cambridge Math. Library (Cambridge University Press, Cambridge, 1990).
[78] W. B., Jones and W. J., Thron, Continued fractions: analytic theory and applications, Encyclopedia of Math. and its Applications 11 (Addison-Wesley, Reading, MA, 1980).
[79] B. C., Kellner, Über irreguläre Paare höhere Ordnungen, Diplomarbeit (Math. Inst., Georg-August-Universität zu Göttingen, Germany, 2002); available at http://www.
[80] A., Khintchine, Metrische Kettenbruchprobleme, Compositio Math. 1 (1935), 361–382.
[81] A., Khintchine, Zur metrischen Kettenbruchtheorie, Compositio Math. 3 (1936), 276–285.
[82] A. Ya., Khintchine, Continued fractions, 2nd edition, translated by P., Wynn (P. Noordhoff, Ltd., Groningen, 1963).
[83] D. E., Knuth, The art of computer programming, Vol. II: Seminumerical algorithms (Addison-Wesley, Reading, MA, 1981).
[84] K., Kolden, Continued fractions and linear substitutions, Archiv for Mathematik og Naturvidenskab 50 (1949), 141–196.
[85] T., Komatsu, A certain power series and the inhomogeneous continued fraction expansions, J. Number Theory 59 (1996), 291–312.
[86] T., Komatsu, On inhomogeneous Diophantine approximation with some quasi-periodic expressions, Acta Math. Hungar. 85 (1999), 311–330.
[87] T., Komatsu, On inhomogeneous Diophantine approximation and the Borweins' algorithm, Far East J. Math. Sci. 12 (2004), 203–224.
[88] T., Komatsu, A proof of the continued fraction expansion of e2/s, Integers 7 (2007), no. A30.
[89] C., Krattenthaler, Advanced determinant calculus, in: The Andrews Festschrift (Maratea, 1998), Sém. Lothar. Combin. 42 (1999), Art. B42q, 67 pp.
[90] L., Kuipers and H., Niederreiter, Uniform distribution of sequences (Wiley-Interscience, New York, 1974).
[91] R. O., Kuzmin, On a problem of Gauss, Dokl. Acad. Sci. USSR (1928), 375–380.
[92] J. C., Lagarias and J., Shallit, Linear fractional transformations of continued fractions with bounded partial quotients, J. Théorie Nombres Bordeaux 9 (1997), 267–279; Corrigendum, J. Théorie Nombres Bordeaux 15 (2003), 741-743.
[93] E., Landau, Bemerkungen zu der vorstehenden Abhandlung von Herrn Franel, Göttinger Nachrichten (1924), 198–206.
[94] S., Lang, Introduction to Diophantine approximations, 2nd edition (Springer-Verlag, New York, 1995).
[95] S., Lang and H., Trotter, Continued fractions for some algebraic numbers, J. Reine Angew. Math. 255 (1972), 112–134; Addendum, J. Reine Angew. Math. 267 (1974), 219-220.
[96] D. H., Lehmer, Euclid's algorithm for large numbers, Amer. Math. Monthly 45 (1938), 227–233.
[97] P., Lévy, Sur les lois de probabilité dont dépendent les quotients complets et incomplets d'une fraction continue, Bull. Soc. Math. France 57 (1929), 178–194.
[98] P., Lévy, Sur le développement en fraction continue d'un nombre choisi au hasard, Compositio Math. 3 (1936), 286–303.
[99] P., Liardet and P., Stambul, Algebraic computations with continued fractions, J. Number Theory 73 (1998), 92–121.
[100] F., Lindemann, Über die Zalh π, Math. Ann. 20 (1882), 213–225.
[101] G., Lochs, Vergleich der Genauigkeit von Dezimalbruch und Kettenbruch, Abh. Hamburg Univ. Math. Sem. 27 (1964), 142–144.
[102] L., Lorentzen, Convergence and divergence of the Ramanujan AGM fraction, Ramanujan J. 16 (2008), 83–95.
[103] L., Lorentzen and H., Waadelend, Continued fractions with applications (North Holland, 1992).
[104] J. H., Loxton and A. J., van der Poorten, Arithmetic properties of certain functions in several variables. III, Bull. Austral. Math. Soc. 16 (1977), 15–47.
[105] S. K., Lucas, Approximations to π derived from integrals with nonnegative integrands, Amer. Math. Monthly 116 (2009), 166–172.
[106] K., MacMillan and J., Sondow, Proofs of power sum and binomial coefficient congruences via Pascal's identity, Amer. Math. Monthly 118 (2011), 549–551.
[107] K., MacMillan and J., Sondow, Divisibility of power sums and the generalized Erdős–Moser equation, Elemente Math. 67 (2012), 182–186.
[108] K., Mahler, Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen, Math. Ann. 101 (1929), 342–366; Corrigendum, Math. Ann. 103 (1930), 532.
[109] E., Maillet, Introduction à la théorie des nombres transcendants et des propriétés arithmétiques des fonctions (Paris, Gauthier-Villars, 1906).
[110] R., Marcovecchio, The Rhin–Viola method for log 2, Acta Arith. 139 (2009), 147–184.
[111] J., McLaughlin, Symmetry and specializability in the continued fraction expansions of some infinite products, J. Number Theory 127 (2007), 184–219.
[112] N., Möller, On Schönhage's algorithm and subquadratic integer GCD computation, Math. Comp. 77 (2008), 589–607.
[113] P., Moree, Diophantine equations of Erdős–Moser type, Bull. Austral. Math. Soc. 53 (1996), 281–292.
[114] P., Moree, A top hat for Moser's four mathemagical rabbits, Amer. Math. Monthly 118 (2011), 364–370.
[115] P., Moree, H., te Riele and J., Urbanowicz, Divisibility properties of integers x, k satisfying 1k + … + (x - 1)k = xk, Math. Comp. 63 (1994), 799–815.
[116] L., Moser, On the diophantine equation 1n + 2n + 3n + … + (m - 1)n = mn, Scripta Math. 19 (1953), 84–88.
[117] H., Niederreiter, Dyadic fractions with small partial quotients, Monatshefte Math. 101 (1986), 309–315.
[118] Ku., Nishioka, Mahler functions and transcendence, Lecture Notes in Math. 1631 (Springer-Verlag, Berlin, 1996).
[119] Ku., Nishioka, I., Shiokawa and J., Tamura, Arithmetical properties of a certain power series, J. Number Theory 42 (1992), 61–87.
[120] I., Niven, A simple proof that π is irrational, Bull. Amer. Math. Soc. 53 (1947), 509.
[121] I., Niven, Irrational numbers, Carus Math. Monographs 11, Math. Assoc. Amer. (John Wiley, New York, NY, 1956).
[122] K., O'Bryant, A generating function technique for Beatty sequences and other step sequences, J. Number Theory 94 (2002), 299–319.
[123] F. W. J., Olver, D. W., Lozier, R. F., Boisvert and C. W., Clark (eds.), NISThandbook of mathematical functions (Cambridge University Press, New York, 2010).
[124] O., Perron, Uber die Approximation irrationaler Zahlen durch rationale, Sitz. Heidelberg. Akad. Wiss. 12A (1921), 3–17.
[125] O., Perron, Die Lehre von den Kettenbmchen, 3rd edition, Bd. I: Elementare Kettenbrüche (B. G. Teubner, Stuttgart, 1954); Bd. II: Analytisch-funktionentheoretische Kettenbrüche (B. G., Teubner, Stuttgart, 1957).
[126] M., Petkovšek, H. S., Wilf and D., Zeilberger, A = B (A. K. Peters, Wellesley, MA, 1996).
[127] A., van der Poorten, A proof that Euler missed… Apery's proof of the irrationality of ζ(3), Math. Intelligencer 1 (1978/1979), 195–203.
[128] A., van der Poorten, Formal power series and their continued fraction expansion, in: Algorithmic number theory, Lecture Notes in Computer Sci. 1423 (Springer-Verlag, Berlin, 1998), pp. 358–371.
[129] A., van der Poorten, Quadratic irrational integers with partly prescribed continued fraction expansion, Publ. Math. Debrecen 65 (2004), 481–496.
[130] A., van der Poorten, Specialisation and reduction of continued fraction expansions of formal power series, Ramanujan J. 9 (2005), 83–91.
[131] A., van der Poorten, Elliptic curves and continued fractions, J. Integer Sequences 8 (2005), paper 05.2.5, 19 pp.
[132] A., van der Poorten, Curves of genus 2, continued fractions, and Somos sequences, J. Integer Sequences 8 (2005), paper 05.3.4, 9 pp.
[133] A., van der Poorten, Hyperelliptic curves, continued fractions, and Somos sequences, in: Dynamics and stochastics, IMS Lecture Notes Monogr. Ser. 48 (Inst. Math. Statist., Beachwood, OH, 2006), pp. 212-224.
[134] A., van der Poorten and J., Shallit, Folded continued fractions, J. Number Theory 40 (1992), 237-250.
[135] A., van der Poorten and J., Shallit, A specialised continued fraction, Can. J. Math. 45 (1993), 1067-1079.
[136] A. J., van der Poorten and C. S., Swart, Recurrence relations for elliptic sequences: every Somos 4 is a Somos k, Bull. London Math. Soc. 38 (2006), 546-554.
[137] M., Prévost, A new proof of the irrationality of ζ(2) and ζ(3) using Padé approximants, J. Comput. Appl. Math. 67 (1996), 219-235.
[138] K., Rajkumar, A simplification of Apéry's proof of the irrationality of ζ(3), Preprint arXiv: 1212.5881 [math. NT] (2012).
[139] G. N., Raney, On continued fractions and finite automata, Math. Ann. 206 (1973), 265-283.
[140] G., Rhin and C., Viola, On a permutation group related to ζ(2), Acta Arith. 77 (1996), 23-56.
[141] R. D., Richtmyer, M., Devaney and N., Metropolis, Continued fraction expansions of algebraic numbers, Numer. Math. 4 (1962), 68-84.
[142] T., Rivoal and W., Zudilin, Diophantine properties of numbers related to Catalan's constant, Math. Ann. 326: 4 (2003), 705-721.
[143] J., Roberts, Elementary number theory: a problem oriented approach (MIT Press, 1978).
[144] A. M., Rockett and P., Szüsz, Continued fractions (World Scientific, Singapore, 1992).
[145] V. Kh., Salikhov, On the irrationality measure of π, Usp. Mat. Nauk. 63 (2008), no. 3, 163-164; English translation, Russian Math. Surveys 63 (2008), 570–572.
[146] A., Schinzel, On some problems of the arithmetical theory of continued fractions, Acta Arith. 6 (1961), 393-413.
[147] A., Schinzel, On some problems of the arithmetical theory of continued fractions II, Acta Arith. 7 (1962), 287-298.
[148] W. M., Schmidt, On badly approximable numbers, Mathematika 12 (1965), 10-20.
[149] W. M., Schmidt, Diophantine approximation, Lecture Notes in Math. 785 (Springer-Verlag, Berlin, 1980).
[150] A., Schönhage, Schnelle Berechnung von Kettenbruchentwicklungen, Acta Informatica 1 (1971), 139-144.
[151] J., Shallit, Real numbers with bounded partial quotients: a survey, L'Enseignement Math. 38 (1992), 151-187.
[152] R., Shipsey, Elliptic divisibility sequences, Ph. D. thesis (Goldsmiths College, University of London, 2000).
[153] P., Shiu, Computation of continued fractions without input values, Math. Comp. 64 (1995), no. 211, 1307-1317.
[154] P., Shiu, A function from Diophantine approximations, Publ. Inst. Math. (Beograd) 65 (1999), 52-62.
[155] Th., Skolem, Über einige Eigenschaften der Zahlenmengen [αn + β] bei irrationalem α mit einleitenden Bemerkungen über einige kombinatorische Probleme, Norske Vid. Selsk. Forh. (Trondheim) 30 (1957), 118-125.
[156] N. J. A., Sloane, The on-line encyclopedia of integer sequences, published electronically at (2013).
[157] K. R., Stromberg, An introduction to classical real analysis (Wadsworth, 1981).
[158] C., Swart, Elliptic curves and related sequences, Ph. D. thesis (Royal Holloway College, University of London, 2003).
[159] B. G., Tasoev, On rational approximations of some numbers, Math. Notes 67 (2000), no. 5–6, 786-791.
[160] R., Tijdeman, Exact covers of balanced sequences and Fraenkel's conjecture, in: Algebraic number theory and Diophantine analysis, Graz, 1998 (de Gruyter, Berlin, 2000), pp. 467-483.
[161] R., Tijdeman, Fraenkel's conjecture for six sequences, Discrete Math. 222 (2000), 223-234.
[162] A. J. H., Vincent, Sur la résolution des équations numériques, J. Math. Pures Appl. 1 (1836), 341-372.
[163] J., Vuillemin, Exact real computer arithmetic with continued fractions, INRIA Report 760 (INRIA, Le Chesnay, France, 1987).
[164] H. S., Wall, Analytic theory of continued fractions (Chelsea Publishing, New York, 1948).
[165] M., Ward, Memoir on elliptic divisibility sequences, Amer. J. Math. 70 (1948), 31-74.
[166] E. T., Whittaker and G. N., Watson, A course of modern analysis, 4th edition (Cambridge University Press, 1927).
[167] A. J., Yee, γ-cruncher – a multi-threaded pi-program, available at
[168] D. B., Zagier, Zetafunktionen und quadratische Körper (Springer-Verlag, New York–Berlin, 1981).
[169] D. B., Zagier, Problems posed at the St Andrews Colloquium (1996), Solutions, 5th day;
[170] D., Zagier, Vassiliev invariants and a strange identity related to the Dedekind eta-function, Topology 40 (2001), 945-960.
[171] D., Zagier, Integral solutions of Apéry-like recurrence equations, in: Groups and symmetries, CRM Proc. Lecture Notes 47 (Amer. Math. Soc., Providence, RI, 2009), pp. 349-366.
[172] S. K., Zaremba, La méthode des ‘bons treillis’ pour le calcul des intégrales multiples, in: Applications of number theory to numerical analysis, Proc. Sympos., Université de Montréal, 1971 (Academic Press, New York, 1972), pp. 39-119.
[173] Y., Zhang, Bounded gaps between primes, Ann. Math. (2013), in press;
[174] W., Zudilin, Well-poised generation of Apéry-like recursions, J. Comput. Appl. Math. 178 (2005), 513-521.
[175] W., Zudilin, Apéry's theorem. Thirty years after, Intern. J. Math. Computer Sci. 4 (2009), 9-19; An elementary proof of Apéry's theorem, Preprint arXiv:math. NT/0202159 (2002).
[176] W., Zudilin, On the irrationality measure of π2, Usp. Mat. Nauk. 68 (2013), no. 6, 171-172; English translation, Russian Math. Surveys 68 (2013), 1133–1135; Two hypergeometric tales and a new irrationality measure of ζ(2), Preprint arXiv: 1310.1526 [math. NT] (2013).