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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)