Originally posted by Acolyte
No, I admit I haven't thought of a counter-example (and your statement may well be correct), I was just trying to suggest that anything involving what happens on the radius of convergence needs to be handled with care.

Have you worked out the answer to 'How smooth?' yet?

Sorry--didn't see it. I'll give it a go in the next couple of days, but I've got a nasty history exam tomorrow that I ought to study for at the moment.