Simultaneous generation of koecher and Almkvist-Granville's Apéry-like formulae

Experimental Mathematics

Volumn 13, Issue 4, 2004, Pages 504-508

  Rivoal, T ^a  

^a UNIVERSITÉ DE CAEN   (France)

Author keywords

Ap ry like series; Generating functions; Riemann Z ta function

Indexed keywords

EID: 14944361601     PISSN: 10586458     EISSN: 1944950X     Source Type: Journal    
DOI: 10.1080/10586458.2004.10504559     Document Type: Article

References (14)

1. G. Almkvist and A. Granville. “Borwein and Bradley’s Apéry-Like Formulae for ζ(4n + 3).” Exp. Math. 8:2 (1999), 197-203.
2. R. Apéry. “Irrationalité de ζ(2) et ζ(3)-” Asterisque 61 (1979), 11-13.
3. K. Ball and T. Rivoal. “Irrationalité d’une infinite de valeurs de la fonction Zêta aux entiers impairs.” Invent. Math. 146:1 (2001), 193-207.
4. J. Borwein and D. Bradley. “Empirically Determined Apéry-Like Formulae.” Exp. Math. 6:3 (1997) 181-194.
5. H. Cohen. “Demonstration de l’Irrationalité de £(3) (d’apres Apéry).” In Sém. de Thiorie des Nombres de Grenoble. Université Joseph Fourier, Grenoble, 1978.
6. H. Cohen. “Généralisation d’une construction de R. Apéry.” Bull. Soc. Math. France 109 (1981), 269-281.
7. R. L. Graham, D. E. Knuth, and O. Patashnik. Concrete Mathematics: A Foundation for Computer Science, 2nd edition. Reading, MA: Addison- Wesley, 1994.
8. M. Koecher. Letter to the Ekiitor. Math. Intelligencer 2 (1980), 62-64.
9. C. Krattenthaler. “A New Matrix Inverse.” Proc. Amer. Math. Soc 124:1 (1996), 47-59.
10. n.” J. Number Theory 13:3 (1981), 355-362.
11. T. Rivoal. “La fonction Zêta de Riemann prend une infinite de valeurs irrationnelles aux entiers impairs.”C. R. Acad. Sci. Paris, Sirie I Math. 331:4 (2000), 267-270.
12. 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.
13. A. van der Poorten. “Some Wonderful Formulas… An Introduction to Polylogarithms.” Queen’s Papers in Pure and Applied Mathematics, (Proc. 1979 Queen’s Number Theory Conference, 1980) 54 (1980), 269-286.
14. W. Zudilin. “Arithmetic of Linear Forms Involving Odd Zêta Values.” To appear in J. Thior. Nombres Bordeaux (2004). Available at http://arXiv.org/abs/math.NT/0206176.