Interpolation of Infinitely Many Points

[l'Hôpital]

This sort of came up the other day:

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

[itex]
f(n) = a_n
[/itex]

?

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

Thanks!

 

[micromass]

See http://mathworld.wolfram.com/RamanujansInterpolationFormula.html or http://mathworld.wolfram.com/RamanujansMasterTheorem.html

The mathworld article isn't very rigorous though and doesn't give the conditions under which this is allowed. So you might want to find a better source.