Talk:Bell series

The uniqueness theorem is a triviality. I would like to see some interesting applications of Bell series. They seem to be pretty boring objects. Why ? If your arithmetic function is integer valued (and most "interesting" arithmetic functions have integer values), then its Bell series must be either rational or have a natural boundary at its radius of convergence (this is a fairly deep theorem, conjectured by Polya, and proved by Carleson I think) ... In other words the Bell series is either "too trivial" to be studied, or in the other direction, too complicated to get anything useful out of it. This is at least how I see it. Reactions ?

-- Maks. —Preceding unsigned comment added by 24.37.24.39 (talk) 02:38, 1 November 2007 (UTC)