08/13/2007, 10:11 PM

bo198214 Wrote:If a function is entire the powerseries converges at each point. If it does not, maybe we can help ourselves by analytic extension but it is not entire then.Hmm, my calculus professors must have glossed over that particular detail. That'd be useful to know. I didn't realize that the only reason a power series would fail to converge for a valid input is because the function is not entire. By the way, entire over the reals or entire over the complex numbers? Does it matter if the only singularities are non-real? (I realize this is a side-topic.)

~ Jay Daniel Fox