Talk:Borel summation

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Comments:

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)

[edit] 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)

[edit] 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)

[edit] 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)