Talk:Zeta function regularization

This article is rated C-class on Wikipedia's content assessment scale. It is of interest to the following WikiProjects:

Physics Low‑importance This article is within the scope of WikiProject Physics, a collaborative effort to improve the coverage of Physics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.PhysicsWikipedia:WikiProject PhysicsTemplate:WikiProject Physicsphysics Low This article has been rated as Low-importance on the project's importance scale. Mathematics Mid‑priority This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics Mid This article has been rated as Mid-priority on the project's priority scale.

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

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

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

In the section called "Relation to other regularizations," we should say that this is similar to the ${\displaystyle Z}$-Transform with ${\displaystyle e^{t}}$, 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 ${\displaystyle Z}$-transform of ${\displaystyle f}$, where ${\displaystyle z=\exp(t)}$."

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

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