Talk:Borel summation

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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)

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