Talk:Abel's theorem

Untitled
The title of this page isn't very specific, since there are a number of mathematical concepts that might be called "Abel's theorem", but it isn't already in use, so I thought I'd take it. Eventually, someone will probably need to disambiguate this and all the other Abel's theorems (and abelian theorems!). For now, at least, it ain't gonna be me! 14/9/05 Your previous version of this theorem which only considered the case of non negative coefficients was correct but could mislead a beginning student. I hope things are clearer now.


 * I think the comments above may have been written by user:Bjcairns; I'm not sure. Michael Hardy 01:41, 28 August 2006 (UTC)

Is "a limit" a specific thing or should it actually read the limit? Thank you. 82.6.114.172 11:08, 4 April 2007 (UTC)


 * It should not say "the", at least as the sentence is now phrased. It is the limit as z approaches 1 from below.  It is not the limit as z approaches something else.  It is one of various possible limits. Michael Hardy 18:18, 4 April 2007 (UTC)

Someone should add a proof to this article. Add in need of expert? JIMOTHY46ct 19:33, 27 December 2007 (UTC)

At the risk of sounding pedantic, I think the choice of dummy variable i in the context of complex numbers is a little unfortunate. Perhaps changing it to k would eliminate the risk of confusion? Jergosh (talk) 20:39, 11 May 2008 (UTC)

Title
I agree with the comment above that the title is not clear. I suggest Abel summation. What do people think? Thenub314 (talk) 16:04, 11 November 2008 (UTC)

Missing reference - Generalisation for divergence to infinity
A generalisation is mentioned that if the series diverges to infinity, than also the Abel summation diverges to infinity. There is no proof in the article and also non of the references includes a proof of this statement. For this statement a reference is needed. Rochard (talk) 23:12, 1 May 2015 (UTC)

It definitely won't work without the assumption that the $$a_k$$'s are real. However it works, by the monotone convergence theorem, whenever $$a_k\geq 0$$. Rochard (talk) 03:41, 2 May 2015 (UTC)