An Apéry-like difference equation for Catalan's constant

Electronic Journal of Combinatorics

Volumn 10, Issue 1 R, 2003, Pages

  Zudilin, W ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3042619680     PISSN: 10778926     EISSN: None     Source Type: Journal    
DOI: 10.37236/1707     Document Type: Article

References (16)

1. R. Apéry, "Irrationalité de ζ(2) et ζ(3)", Astérisque 61 (1979), 11-13.
2. W.N. Bailey, Generalized hypergeometric series, Cambridge Math. Tracts 32, Cambridge Univ. Press, Cambridge, 1935; 2nd reprinted edition, Stechert-Hafner, New York-London, 1964.
3. K. Ball and T. Rivoal, "Irrationalité d'une infinité de valeurs de la fonction zêta aux entiers impairs", Invent. Math. 146:1 (2001), 193-207.
4. F. Beukers, "A note on the irrationality of ζ(2) and ζ(3)", Bull. London Math. Soc. 11:3 (1979), 268-272.
5. H. Cohen, "Accélération de la convergence de certaines récurrences linéaires", Séminaire de Théorie des nombres de Bordeaux (Année 1980-81), exposé 16, 2 pages.
6. W.B. Jones and W. J. Thron, Continued fractions. Analytic theory and applications, Encyclopaedia Math. Appl. Section: Analysis 11, Addison-Wesley, London, 1980.
7. M. Petkovšek, H. S. Wilf, and D. Zeilberger, A = B, A.K. Peters, Ltd., Wellesley, MA, 1997.
8. A. van der Poorten, "A proof that Euler missed... Apéry's proof of the irrationality of ζ(3)", An informal report, Math. Intelligencer 1:4 (1978/79), 195-203.
9. T. Rivoal and W. Zudilin, "Diophantine properties of numbers related to Catalan's constant", Math. Annalen (2003), to appear; Prépubl. de l'Institut de Math. de Jussieu, no. 315 (January 2002), 17 pages.
10. T. Rivoal and W. Zudilin, "Diophantine properties of numbers related to Catalan's constant", Math. Annalen (2003), to appear; Prépubl. de l'Institut de Math. de Jussieu, no. 315 (January 2002), 17 pages.
11. L. J. Slater, Generalized hypergeometric functions, Cambridge Univ. Press, Cambridge, 1966.
12. 4", Preprint (April 2002), Russian Academy of Sciences, M.V. Keldysh Institute for Applied Mathematics, Moscow, 2002, 59 pages; available at http://www.wis.kuleuven.ac.be/applied/intas/Art5.pdf.
13. V. V. Zudilin [W. Zudilin], "Difference equations and the irrationality measure of numbers", Collection of papers: Analytic number theory and applications, Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.] 218 (1997), 165-178.
14. V. V. Zudilin [W. Zudilin], "Cancellation of factorials", Mat. Sb. [Russian Acad. Sci. Sb. Math.] 192:8 (2001), 95-122.
15. W. Zudilin, "Well-poised hypergeometric service for diophantine problems of zeta values", Actes des 12èmes rencontres arithmétiques de Caen (June 29-30, 2001), J. Théorie Nombres Bordeaux, to appear.
16. W. Zudilin, "A few remarks on linear forms involving Catalan's constant", Chebyshevskiǐ Sbornik (Tula State Pedagogical University) 3:2 (4) (2002), 60-70; English transl., E-print http://arXiv.org/math.NT/ 0210423 (October 2002).