Talk:Zeta function regularization

Physics Low‑importance

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On the face of this this article appears to be rubbish. Can anyone make sense of it? Billlion 15:53, 8 November 2005 (UTC)[reply]

I cleaned up the format and added some links, but it's not my field and I can't say anything about the content. It seems to closely follow Casimir_effect#Calculation, so maybe it could be merged or redirected there. Tom Harrison ^(talk) 17:01, 8 November 2005 (UTC)[reply]

I improve some explanations and make clear the relation to Casimir effect. --Enyokoyama (talk) 12:53, 6 January 2013 (UTC)[reply]

Reference to $Z$ -Transform[edit]

I believe the reference here to the $Z$ -Transform is inconsistent with the contemporary definition. In the Wikipedia article on the transform, we have defined the sum to be:

X(z)=\sum _{n=-\infty }^{\infty }x[n]z^{-n}\

In the section called "Relation to other regularizations," we should say that this is similar to the $Z$ -Transform with $e^{t}$ , where the exponent is positive, not negative. Also, to say that this is the transform itself may not be strictly correct. I suggest that we say "This is closely related to the $Z$ -transform of $f$ , where $z=\exp(t)$ ."

Definition[edit]

The "Definition" section of this article doesn't seem to give a definition of Zeta function regularization. Rather, it gives an example in the physical world. I have never opened a math textbook and seen "DEFINITION OF DERIVATIVE: As an example of a derivative, consider velocity. . . . " Shouldn't this article begin with an explicit definition, and then present examples?

Furthermore, this page seems entirely inaccessible without significant physical knowledge. Seeing as it is a mathematics article, I find this annoying. Eebster the Great (talk) 02:09, 15 January 2009 (UTC)[reply]

But not sufficient, to modify the definition slightly. The connection with the physical description latter has improved a little. --Enyokoyama (talk) 09:42, 14 October 2012 (UTC)[reply]

Dear! Ardehali. I appreciate your point out about its history.--Enyokoyama (talk) 14:33, 20 January 2013 (UTC)[reply]

Elizalde’s proposal[edit]

Thanks Karl-H for adding description about Elizalde's proposal. As soon as you add them I translate into Japanese. In English its reference "renormalization" contains Elizalde's proposal but In Japanese corresponding article titled "Kurikomi," which is very beautiful and useful word meaning the properties of renormalization, does not contain Elizalde's proposal. Somehow, I will describe them.--Enyokoyama (talk) 14:14, 20 March 2013 (UTC)[reply]

Oh! I see! Elizalde himself had written the article, Zeta-function method for regularization. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Zeta-function_method_for_regularization&oldid=29548 .--Enyokoyama (talk) 13:53, 22 March 2013 (UTC)[reply]

Dear 85.85.96.167 Thanks for your adding some descriptions--Enyokoyama (talk) 11:53, 23 June 2013 (UTC)[reply]

Reference to Z {\displaystyle Z} -Transform[edit]

Definition[edit]

Elizalde’s proposal[edit]

Reference to $Z$ -Transform[edit]