A quadratic recurrence of Faltung type
Published online by Cambridge University Press: 24 October 2008
Extract
We write and x1 = 1. In a recent paper (3), Stein and Everett consider the sequence defined by
and investigate whether
tends to a limit as n → ∞. The case b = 0 has a combinatorial interpretation (see (1)) and, in (2), they use this to prove that xn → e−1 in this case. Even for positive integral b, the number Sn has no known combinatorial interpretation, but they prove (3) that xn → x under the hypothesis that Sn+1Sn−1 ≥ Sn i.e. that Sn is convex. By computation and induction, they prove this hypothesis for b = k/5, where k = 1, 2,…, 50.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 88 , Issue 2 , September 1980 , pp. 193 - 197
- Copyright
- Copyright © Cambridge Philosophical Society 1980
References
REFERENCES
- 2
- Cited by