Talk:Beta function

message: On the page it says:
 \mathrm{\Beta}(x,y) = \frac{1}{y}\sum_{n=0}^\infty(-1)^n\frac{(y)_{n+1}}{n!(x+n)}\!
Should it not say: MATH or is the subscript a notation I'm not familiar with? 
OrangeDog 20:32, 1 September 2006 (UTC)
thread_title:  Equation error? 

message: What does Re(x) mean? It's used in the text but not explained. —The preceding unsigned comment was added by 136.142.141.195 (talk) 21:46, 7 February 2007 (UTC)
replies: text: No, Re(x) means the real part of the complex number x. Fredrik Johansson 16:12, 22 March 2007 (UTC)
thread_title:  unexplained notation-- Re(x) 

message: Is \int_t^z \frac{dx}{(x-t)^\alpha(z-x)^{1-\alpha}} an accurate representation of B(1-\alpha,\alpha), and therefore probably easily generalized to the full beta function?   It comes up in solving Abel's integral equation f(x)=\int_0^x\frac{\phi(t)}{(x-t)^\alpha}dt.  I just don't have the energy to prove it at the moment, but if it is, I'm sure its a useful representation. —The preceding unsigned comment was added by Ub3rm4th (talk • contribs) 23:35, 25 April 2007 (UTC)
thread_title:  Alternative integral representation 

message: Should there be a bit more in the introduction explaining what the beta function is used for in non-maths speak?  I think this would be helpful. For example we could add something about it being used as a normalisation factor in the beta distribution. Grj23 (talk) 08:37, 21 May 2008 (UTC)
thread_title:  Introduction 

message: Alright, there's just too much beta functions going around. This page should be moved to Euler beta function, and this one be turned into a disambiguation page similar to:
Beta function may refer too:
*Beta function (physics), which details the running of the coupling strengths in high-energy physics.
*Dirichlet beta function, also know as the Catalan beta function, which is closely related to the Riemann zeta function.
*Euler beta function, the Euler integral of the first kind, studied by Euler and Legendre.
*Others ...

I've contacted WP:PHYS and WP:WPMATH. Headbomb {ταλκκοντριβς – WP Physics} 02:29, 9 September 2009 (UTC)
replies: text: Actually, I disagree: this (Euler) function should remain the default meaning of "beta function". If you think of Gamma function, that for mathematicians has a default meaning, and everyone knows what "the" Gamma function is. I believe the same can be said for the beta function. So the configuration with beta function (disambiguation) and this page as it stands would be better. Charles Matthews (talk) 08:50, 9 September 2009 (UTC)
replies: text: I concur with Charles Matthews. RobHar (talk) 11:04, 9 September 2009 (UTC)
replies: text: I concur too. I think the most common beta function is the Euler beta function, and it should be the default page when someone types "beta function" into Wikipedia. --Robin (talk) 18:59, 9 September 2009 (UTC)
replies: text: Really? I recall seeing both the Euler and Dirichlet functions at about equal proportion. If no one else abides towards my direction, I'll create beta function (disambiguation) either tonight or tomorrow. Headbomb {ταλκκοντριβς – WP Physics} 19:09, 9 September 2009 (UTC)
replies: text: DAB created. Headbomb {ταλκκοντριβς – WP Physics} 07:32, 11 September 2009 (UTC)
thread_title:  Disambiguation 

message: The Dirichlet distribution article makes use of a multivariate Beta function defined as:
 \Beta(\mathbf{x}) = \int_{\Delta^n} \left( \prod_{i=1}^n \alpha_i^{x_i-1} \right) d \alpha
Where \mathbf{x} \in \mathbb{R}^n and \Delta^n is the unit n-simplex. (There is some abuse of the integration notation because the components of the \alpha vector are dependent through the simplex constraints, so there may be a more correct way of writing this).
It would make sense to include such a definition here. 130.49.222.251 (talk) 16:30, 24 September 2010 (UTC)
thread_title:  Multivariate Beta Function? 

message: What is the motivation for this function? For example, Gamma function is a continious case of factorial function and thus is usefull in some functional equations. Is there a informal motivation for Beta function?  — Preceding unsigned comment added by Comecra (talk • contribs) 14:03, 7 June 2012 (UTC)
replies: text: I have just read such a comment in the book "The Elegant Universe".  — Preceding unsigned comment added by 83.50.13.241 (talk) 22:29, 13 January 2013 (UTC)
replies: text: I definitely support the sentiment that this article is distinctly lacking in purpose. That's great that some mathematicians have described the function, but I am left with absolutely no idea as to what it describes or when it might be used. The only hint is that it's listed as a statistics article. Owen214 (talk) 01:33, 13 April 2015 (UTC)
thread_title:  Motivation for Beta function. 

message: There was a recent unfavorable comment on the quality of the graph on this page (and the MathWorld analogue) on the math-fun discussion list. The picture  was given as a comparison and an example of 'how it should look'.
I'm expert on neither the beta function nor graphics, but I thought this was worth mentioning for those who are knowledgeable about either.
CRGreathouse (t | c) 01:07, 23 July 2013 (UTC)
thread_title:  Plot 

message: ::
\Beta(x,y) \cdot \Beta(x+y,1-y) =
  \dfrac{\pi}{x \sin(\pi y)}
\!
\!
There is a problem with the above property. The denominator can become zero in some cases.
84.88.76.16 (talk) 14:44, 30 October 2013 (UTC)
thread_title:  Beta property 

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thread_title:  External links modified 

message: I can't seem to make the latter equation of the software implementation to work. For x -> 1, it's supposed to go to a non-zero value I(x,a,b)>0, but the BetaPdf goes always to zero. Therefore the equation cannot be true. I was actually looking for an answer to that, so I don't have a proposal for a solution available.
Tbackstr (talk) 10:39, 24 April 2017 (UTC)
thread_title:  Software implementation 

message: I put the properties in the form of a list, because there was some ambiguity, for instance point 3 refers to x,y as integer arguments and it was not clear if this hypothesis applied to the following lines too.
Xtquique (talk) 06:47, 23 June 2020 (UTC)
replies: text: I have reverted, because encyclopedia articles should be written in prose, not as bulleted lists.  (I left a longer comment in my edit summary.) --JBL (talk) 13:56, 23 June 2020 (UTC)

text: I have started improving it, more help is welcome. --JBL (talk) 15:53, 23 June 2020 (UTC)

text: I removed the following sentence, because I couldn't figure out what it referred to:   If anyone has a clue, feel free to reinsert it in an appropriate spot. --JBL (talk) 16:38, 23 June 2020 (UTC)
thread_title: List

message: It is unclear what this plot actually shows.  Is it perhaps the beta function in the complex plane of one argument for some constant but unspecified value of the other argument? catslash (talk) 01:05, 29 June 2023 (UTC)
replies: text: Done. catslash (talk) 21:43, 31 July 2023 (UTC)
thread_title: Second plot

message: The beta function can be written as an infinite sum ... (where (z)n is the rising factorial).
But (z)n is the notation for the falling factorial.
So, is the notation wrong, or should the text say "falling factorial"?
I haven't been able to find another source that clarifies this. Johndawson45 (talk) 12:40, 13 December 2023 (UTC)
replies: text: I see elsewhere that the Pochhammer function, written as (z)n is used to represent either the rising or the falling factorial! Perhaps Knuth's underline and overline notations should be used for clarity. Johndawson45 (talk) 12:45, 13 December 2023 (UTC)
thread_title:  Incorrect notation?