Irrationality measures for the series of reciprocals from recurrence sequences

Journal of Number Theory

Volumn 96, Issue 2, 2002, Pages 275-292

  Matala aho, Tapani ^a   Prévost, Marc ^b  

^a UNIVERSITY OF OULU   (Finland)

^b UNIVERSITÉ DU LITTORAL CÔTE D OPALE   (France)

Author keywords

Fibonomials; Irrationality measure; Pad approximation; Q hypergeometric; Recurrence

Indexed keywords

EID: 0036801204     PISSN: 0022314X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-314X(02)92795-2     Document Type: Article

References (18)

1. R. André-Jeannin, Irrationalité de la somme des inverses de certaines suites récurrentes, C. R. Acad. Sci. Paris, Sér. I Math. 308 (1989), 539-541.
2. G. E. Andrews, "The Theory of Partitions," Addison-Wesley, London, 1976.
3. J.-P. Bézivin, Indépendance linéaire des valeurs des solutions transcendantes de certaines équations fonctionnelles, Manuscripta Math. 61 (1988), 103-129.
4. J.-P. Bézivin, Plus petit commun multiple des termes consécutifs d'une suite récurrente linéaire, Collect. Math. 40 (1989),1-11.
5. J.-P. Bézivin, Indépendance linéaire des valeurs des solutions transcendantes de certaines équations fonctionnelles II, Acta Arith. 55 (1990), 233-240.
6. n + r)), J. Number Theory 37 (1991), 253-259.
7. P. B. Borwein, On the irrationality of certain series, Math. Proc. Cambridge Philos. Soc. 112 (1992), 141-146.
8. P. Bundschuh and K. Väänänen, Arithmetical investigations of a certain infinite product, Compositio Math. 91 (1994), 175-199.
9. n, Ann. Math. 15 (1913-1914), 30-70.
10. Deleted in proof.
11. D. Duverney, K. Nishioka, K. Nishioka, and I. Shiokawa, Transcendence of Rogers-Ramanujan continued fraction and reciprocal sums of Fibonacci numbers, Proc. Japan Acad. Ser. A Math. Sci. 73 (1997), 140-142.
12. A. O. Gel'fond, Functions which take on integral values (Russian), Mat. Zametki 1 (1967), 509-513 (Engl. transl. Math. Notes 1 (1967), 337-340).
13. T. Matala-aho, Remarks on the arithmetic properties of certain hypergeometric series of Gauss and Heine, Acta Univ. Oulu. Ser. A Sci. Rerum Natur. 219 (1991), 1-112.
14. T. Matala-aho and K. Väänänen, On approximation measures of q-logarithms, Bull. Austral. Math. Soc. 58 (1998), 15-31.
15. Y. Nesterenko, Modular functions and transcendence questions (Russian), Mat. Sb. 187 (1996),65-96.
16. K. Nishioka, "Mabler Functions and Transcendence," Lecture Notes in Mathematics, Vol. 1631, Springer, Berlin, 1996.
17. tn J. Number Theory 73 (1998), 139-161.
18. K. Väänen, On series of reciprocals of Lucas sequences, Math. Univ. Oulu, 1997, prepnnt.