Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

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

How can I use the identity $$\sum_{n=0}^\infty \frac{\tau^n}{n!} = \lim_{y \to \infty} \left( 1 + \frac{\tau}{y} \right)^y$$ to find an exponential Diophantine representation of the factorial?

I was hoping to use a very large value of $y$ (so that the RHS is within an integer of the actual number) and expand with binomial theorem then extract the $\tau^k$ term to get at $k!$ but since we have $\frac{1}{k!}$ this is impossible.

I am really stuck! Any clues on how to do this? Thank you.

share|cite|improve this question

Your Answer

 
discard

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

Browse other questions tagged or ask your own question.