MathOverflow is a question and answer site for professional mathematicians. 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

Given a sequence of complex numbers $a_n$ with $n\in\mathbb{N}$, is it possible to find an analytic (or meromorphic) function that interpolates this sequence in the sense that $f(n)=a_n$?

If this is not always possible, what sort of conditions on the sequence could guarantee the existence of such an $f$?

share|cite|improve this question
See – Yemon Choi Dec 1 '09 at 1:12

There is a classic result of Ramanujan known as his Master Formula which Wolfram has here:

To summarize briefly (and coarsely): if the values you want to interpolate do not grow faster than the gamma function, things will be ok. If they do grow faster than that, his formula doesn't converge, so you'll have to find another technique.

share|cite|improve this answer
There are other references easily available on the web, hopefully a search for Ramanujan's master formula--maybe on MathSciNet--will help you find anything you need. – Ben Weiss Dec 1 '09 at 1:26
It seems Google of Ramanujan "master theorem" works better than Ramanujan "master formula" – Gerald Edgar Dec 1 '09 at 13:09

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.