Talk:Function of several complex variables/Archive 1: Difference between revisions

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{{archive}}

== Vote for new external link ==

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=== References ===

{{reflist|group=Ifaptmbrttp}}

== Unclear sentence ==

In the section '''Radius of convergence of power series''', this sentence:

"''In the power series <math>\sum_{k_1,\dots,k_n=0}^\infty c_{k_1,\dots,k_n}(z_1-a_1)^{k_1}\cdots(z_n-a_n)^{k_n}\ </math>, it is possible to define ''n'' combination of <math>r_\nu</math><ref group=note>This combination may not be unique.</ref>

:"''<math>\begin{cases}

\text{Absolutely converge on}\ \{ z=(z_1, z_2, \dots, z_n) \in {\Complex}^n \mid | z_\nu - a_\nu | < r_\nu, \text{ for all } \nu = 1,\dots,n \}\\

\text{Does not absolutely converge on}\ \{ z=(z_1, z_2, \dots, z_n) \in {\Complex}^n \mid | z_\nu - a_\nu | > r_\nu, \text{ for all } \nu = 1,\dots,n \}

\end{cases}</math>

''"

is very poorly worded and makes no sense in normal English. I hope someone knowledgeable about this subject who is also familiar with English can rewrite this so that it is readable and accurate.

I'm '''guessing''' that what is '''meant''' is this:

... it is possible to define ''n'' positive real numbers <math>r_\nu</math> such that the power series

<math>\begin{cases}

\text{is absolutely convergent on}\ \{ z=(z_1, z_2, \dots, z_n) \in {\Complex}^n \mid | z_\nu - a_\nu | < r_\nu, \text{ for all } \nu = 1,\dots,n \}\\

\text{and is not absolutely convergent on}\ \{ z=(z_1, z_2, \dots, z_n) \in {\Complex}^n \mid | z_\nu - a_\nu | > r_\nu, \text{ for all } \nu = 1,\dots,n \}

\end{cases}</math>

(Is that right?) This would read better if we could get rid of the "cases" curly bracket and just use normal English here.[[Special:Contributions/128.120.234.237|128.120.234.237]] ([[User talk:128.120.234.237|talk]]) 06:09, 29 December 2020 (UTC)

:Thank you for the advice. I tried to fix it.--[[User:SilverMatsu|SilverMatsu]] ([[User talk:SilverMatsu|talk]]) 02:04, 31 December 2020 (UTC)

== Proposed merge of [[Several complex variables]] into [[Complex analysis]] ==

Properly belongs as one article, functions of one complex variable are a special case of functions of several complex variables and both should be discussed in the same article with complex analysis. Furthermore, [[complex variables]] is an unacceptable and confusing DAB page which should also redirect here. If those articles need a DAB, it can be accomplished with a hat note and a link to a new [[complex variables (disambiguation)]]. Size is not an issue. [[User:Footlessmouse|Footlessmouse]] ([[User talk:Footlessmouse|talk]]) 07:03, 31 October 2020 (UTC)

:{{Ping|Footlessmouse}} Nice to me you. I'm in support of inserting Several complex variables into the complex analysis page, but please wait a bit for page consolidation.In complex analysis, holomorphic is a characteristic property, which is different from several real variables.In other words, we need to write about the differences from several real variables.In order to clarify the difference from complex analysis, it may be possible to integrate several pages included in [[:Category:Several complex variables]], or to have duplicate contents.--[[User:SilverMatsu|SilverMatsu]] ([[User talk:SilverMatsu|talk]]) 13:11, 1 November 2020 (UTC)