# Interpolation of Infinitely Many Points

1. Mar 12, 2013

### l'Hôpital

This sort of came up the other day:

Given a sequence of monotonically decreasing points, $a_n$, such that $a_n \rightarrow 0$ does there exist an analytic $f$ on ℝ such that

$f(n) = a_n$

?

I figured there should be some sort interpolation theory on this, but I haven't found anything yet.

Thanks!

2. Mar 13, 2013

### micromass

Staff Emeritus