Meital Posted September 14, 2005 Share Posted September 14, 2005 what is the radius of convergence of the sum (n=0 to infinity) of z^(n!) ? Link to comment Share on other sites More sharing options...
matt grime Posted September 14, 2005 Share Posted September 14, 2005 Certainly it converges for all |z|<1 since it is a subseries of the series z^n and certainly it diverge when z=1. But a more interesting exercise: show it diverges for a dense set of points on the circle |z|=1, thus it can how no continuation beyond the unit circle. This is what makes it an intersting function. Link to comment Share on other sites More sharing options...
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