Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top
  • I start learning about generating functions , so I ask , for example , what all the deduces that a generatingfunctionologist can make for a sequence like :

  • $x_{0}= c$ (some constant , say for example 1).

  • $x_{n+1}=x_{n}+\frac{1}{x_{n}}$

share|cite|improve this question
See also: – Aryabhata Sep 11 '11 at 14:49
@Aryabhata, Grrrr... I spent the last 10 minutes of my life searching for this page, finally found it, and came back on this one to discover your comment. :-) – Did Sep 11 '11 at 15:14
@Didier: Sorry :-) – Aryabhata Sep 11 '11 at 20:55
up vote 3 down vote accepted

Not sure that generating functions enter the picture here but the asymptotics of $(x_n)$ is clear: first prove that $x_n\to+\infty$, then note that $x_{n+1}^2=x_n^2+2+1/x_n^2$, and that this implies first that $x_n^2=2n+o(n)$ and then that $x_n^2=2n+\frac12\log n+o(\log n)$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.