Talk:Differentiation of Power Series

As already discussed on p.ms talk page, and brought up by abcxyz, we need to justify termwise differentiation. One possible track is to start introducing formal power series, and then showing that such a power series converges on the open disc with the convergence radius, and then that its formal (termwise) derivative also has the same radius of convergence. --Lord_Farin 02:55, 8 March 2012 (EST)


 * It is quite easy to show that the termwise derivative of a power series has the same radius of convergence as the original power series. (This can be proved in the same way as this statement.) The theorem stated in this article follows by repeated application of Derivative of Complex Power Series. Maybe this page should be called "Repeated Derivative of Complex Power Series" as a corollary to Derivative of Complex Power Series? Abcxyz 23:44, 8 March 2012 (EST)


 * Just don't remove any existing material, or change it so that its scope is no longer relevant to its linked pages.
 * If you're really keen on expanding these analysis results to include the complex plane, perhaps you'd like to start with the fundamentals and work up? --prime mover 01:06, 9 March 2012 (EST)