Talk:Borel summation

I think, there is an error in the formula. Instead of (k-1)! in

Define the Borel transform $$\mathcal{B}y$$ of $$y$$ by $$\sum_{k=0}^\infty \frac{y_k}{(k-1)!}t^{k-1}.$$

certainly one would expect (k+1)!:

Define the Borel transform $$\mathcal{B}y$$ of $$y$$ by $$\sum_{k=0}^\infty \frac{y_k}{(k+1)!}t^{k+1}.$$

Gottfried Helms --Gotti 15:06, 21 August 2006 (UTC)

I'm almost certainly the person who made the original k-1 error here. Before I edit I want to also find a good link for a references section. Sigfpe 23:21, 27 November 2006 (UTC)

A worked example would be good
Perhaps
 * $$\sum^\infty_k 2^k = 1/(1-2) = -1$$

or
 * $$\sum^\infty_i i = -1/12$$

? --njh 04:08, 8 September 2006 (UTC)

link to laplace-transfomation
Following the link to the laplace-transformation, it seems, that in cases, where we do not deal with frequencies and time-series, a Borel-summation is not applicable. But I know, that Borel-sums were computed without the transformation into time-series. (simply summation of real-values sequences, for instance in K.Knopp and G.H.Hardy).

So, what's going on here?

--Gotti 10:29, 12 March 2007 (UTC)

WikiProject class rating
This article was automatically assessed because at least one WikiProject had rated the article as start, and the rating on other projects was brought up to start class. BetacommandBot 09:44, 10 November 2007 (UTC)

cleanup-rewrite
As already remarked on 21 August 2006, this article contains erroneous definitions from the start and no solid references. Therefore "cleanup-rewrite". A good starting point for a rewrite from scratch would be: http://www.nbi.dk/~polesen/borel/node7.html --que, 200808071740

Why Nicholas Katz?
Why is the quote attributed to Nicholas M. Katz, when the citation is clearly from M. Katz (as e.g. google books will confirm)? 129.199.98.61 (talk) 16:50, 26 October 2010 (UTC)


 * Good point. Someone must have been too aggressive in trying to find a full name. Fixed. Ozob (talk) 23:20, 26 October 2010 (UTC)