Talk:Radius of convergence

message: Why must 1/L and 1/C be used for the radius of convergence? Why can't we invert the equations as they stand?  For example  {1 \over L} = R = \mbox{Radius Of Convergence} = \lim_{n\rightarrow\infty} \left| \frac{c_{n}}{c_n+1} \right|  . Why can't we put that up. Do C and L have special uses?? - Fresheneesz
::Alright that it, I'm freaking changing it. If someone wants to change it back, discuss it *here*. Fresheneesz 08:25, 27 March 2006 (UTC)
replies: text: A possible reason is consistency with root test and ratio test. But feel free to change it. -- Jitse Niesen (talk) 12:03, 27 March 2006 (UTC)
replies: text:  Ratio test doesn't have a letter assocaited with it on the page at least (anymore?). But I don't want to change it if people actually use the letters L or C to mean something. If its 100% arbitrarily used.... Well, yea i guess it would be a good parallel. I think i'll fix it up so it is less arbitrary. Fresheneesz 09:23, 28 March 2006 (UTC)
thread_title: L and C: root and ratio test

message: Since it looks as if a "radius of convergence" is a term only used for power series, and that page already has something on radius of convergence, it seems only natural to merge the two. Any comments? Fresheneesz 10:29, 29 March 2006 (UTC)
replies: text: I disagree. This is an important enough concept to warrant its own article. Besides, the radius of convergence is only for power series of one variable, while power series can be in many variables. Oleg Alexandrov (talk) 17:42, 29 March 2006 (UTC)
replies: text: I bet in power series of many variables one has many radii to define a polydisc of convergence, or even polyballs("Hartogs stuff') or more general cartesian products of balls of different dimension.Rich 21:33, 31 October 2006 (UTC)
thread_title: Merge with power series

message: "The root test is defined as: C=..."  - That doesn't make sense.  A test is not an equation, nor is it a real number.  Also for "ratio test" later.  --Zerotalk 08:59, 14 August 2006 (UTC)
replies: text: I agree. I have no idea what is being said. Can someone fix this? A5 21:06, 31 October 2006 (UTC)
thread_title:  odd wording 

message: Suppose one had a power series w/radius of conv = 1, say, around z=0, say. If z were allowed to be quaternionic, then the boundary of convergence would be a 3 sphere of rad 1. I bet the subset of the boundary where the series converges could be quite beautiful and fascinating. Does anyone know of results/research in this area? It would be a great addition to put in this article.Rich 07:47, 25 September 2006 (UTC)
thread_title: 3-sphere of convergence?

message: Can please someone do a few more concrete examples of finding out the radius of convergence for when z is complex and when it is real and a few special cases. It will help a lot.  —Preceding unsigned comment added by 128.100.194.208 (talk) 16:07, 4 October 2010 (UTC)
replies: text: What would you like examples of? What sorts of series? (Please keep in mind WP:NOTTEXTBOOK.) Ozob (talk) 22:15, 4 October 2010 (UTC)
thread_title:  More examples  

message: Can someone actually do the example of showing and actually working out the steps that the power series Σ zn/n converges at every point of the unit circle except at z=1, that the series Σ zn/n2 converges at every point of the unit circle and that Σ nzn does not converges on any point of the unit circle. It is easy to find the radius of convergence but how to determine what happens on the radius of convergence.
What is special here is that all of the series mentioned have a radius of convergence of 1.
A good idea would also be to include these 3 examples in the relevent section as they are an interesting example due to their 3 properties.  —Preceding unsigned comment added by 64.56.250.36 (talk) 07:38, 11 October 2010 (UTC)
thread_title:  Convergence on the boundry. 

message: This section states "The limit involved in the ratio test is usually easier to compute, and when that limit exists, it shows that the radius of convergence is finite."  Surely this is incorrect?  It's possible that the ratio tends to some <1 value irrespective of the relevant variable, no? 188.74.64.241 (talk) 10:56, 20 March 2016 (UTC)
replies: text: I don't understand your objection, but I believe the article is correct.  Ozob (talk) 16:40, 20 March 2016 (UTC)
thread_title:  Theoretical radius - error?