Talk:Error function

message: Is there any source for this approximation mentioned in the "Applications" section article? This looks more like a Gaussian PDF than a CDF for the values of A and B I tried:
: 
\Pr[X\leq L] = \frac{1}{2} + \frac{1}{2}\operatorname{erf}\left(\frac{L-\mu}{\sqrt{2}\sigma}\right) \approx A \exp \left(-B \left(\frac{L-\mu}{\sigma}\right)^2\right)
where A and B are certain numeric constants.  — Preceding unsigned comment added by 194.94.96.194 (talk) 10:27, 19 November 2016 (UTC)
thread_title:  Source for approximation 

message: Please have someone competent recreate this page.  Your error function table of numerical values is WRONG, which is both shockingly inexcusable and could wreak havoc if people actually use it.  You can easily verify it is wrong by checking any standard handbook, e. g. CRC handbook of chemistry and physics, CRC math handbook, Lange's handbook of chemistry.
Please fix it, and please permanently bar whomever posted it from contributing to Wikipedia.  I realize from what I read here that quality control is anathema, but PLEASE, people really might use this to make important decisions!
Andy Cutler
184.78.143.36 (talk) 05:40, 14 June 2010 (UTC)
replies: text: The above is possibly a moron's joke; anyway the values reported in the article are correct, as anybody can check. --pma 18:27, 14 June 2010 (UTC)

text: I was surprised to see a table like that here. Those used to be valuable pieces of information in the past, but now they only take up space. And if you do so, you will need to be consistent and do the same for https://en.wikipedia.org/wiki/Logarithm, https://en.wikipedia.org/wiki/Gamma_function, and https://en.wikipedia.org/wiki/Logistic_function Anne van Rossum (talk) 11:51, 19 December 2013 (UTC)
replies: text: I agree that tabulated values are a waste of space these days. — Steven G. Johnson (talk) 15:09, 19 December 2013 (UTC)
thread_title:  FUBAR!!! ERROR in the ERROR FUNCTION!  

message: Sorry, there is no Spanish page for this article, so i'm forced to ask here =)
erf and erfc are "Bounded functions"??
In the sense that, for instance -1<erf<1  and 0<erfc<2..
Is this true? Why not mention it?
I'm reading a text here, (Haykin's Communications Systems) that says that erfc is upper bounded by erfc(u)<exp(-u^2)/sqrt(pi*u)  for huge positive values of "u"
I don't see how this relates to the graphic in which the maximum value is just "2" for big negative arguments and "0" for big positive ones
Thanks very much, you all rock n' roll big time!
Ugo O.
:Yes they are bounded (for real values of x at least) as well as a lot of other things that could also be mentioned but weren't.
:For large values of u erfc goes to zero and the formula you refer to seems (I didn't check) to give you an upper bound that shows how fast it is going to zero (which is very fast, as the second table in the article also shows). AlexFekken (talk) 10:51, 28 June 2012 (UTC)
thread_title:  Bounded function/s? 

message: Hello. I see the error function is said to be "non-elementary". What does this mean, exactly? I was under the impression that the division of functions into elementary and special functions, and other categories, was pretty arbitrary. Maybe someone can clarify this point. Is there a more precise category that erf falls into? I'm grasping at straws here -- maybe some group or other algebraic structure? Happy editing, Wile E. Heresiarch 04:09, 17 Feb 2004 (UTC)
replies: text: Maybe it's somewhat arbitrary, but it means you can't express it in terms of the usual functions studied in first-year calculus by using the usual arithmetic operations and composition and inversion of functions.  Michael Hardy 22:31, 17 Feb 2004 (UTC)
replies: text: Why is this?  Perhaps somebody could add a proof.  21:44, 30 Oct 2004 (UTC)
replies: text: I agree: it would be a good article topic.  I'm not up on the details.  Maybe there's already such an article here; I'll see if I can find it. Michael Hardy 21:06, 30 Oct 2004 (UTC)
replies: text: It's really not that elusive. Just go to the wikipedia site "Elementary function".
It means its antiderivative cannot be expressed as an elementary function. Think of a function who's derivative is the error function, (hint) there isn't one just like sin(x^2) that is why we use series to approximate these functions.  — Preceding unsigned comment added by 75.110.96.120 (talk) 01:06, 20 January 2014 (UTC)
thread_title:  Non-elementary? 

message: Question: What is the relationship between the "complementary error function" and the "inverse error function"? 
Ohanian 06:22, 2005 Apr 5 (UTC)
Answer: I'm not aware of any relationship between the two.  The complementary error function is simply a scaled version of the error function to find the area under the tail of the gaussian pdf above the value x, rather than integrate between 0 and x.  The inverse error function is what most people would expect an inverse function to be: erf-1( erf( x ) ) = x. Bencope 18:15, 21 June 2006 (UTC)
thread_title:  Complementary versus invserse 

message: Erf is odd. Why use the word "evidently"?
We sometimes say something is "evidently" true when we make this assertion by observation instead of through some proof.  I don't believe it matters whether it is included or not.jgoldfar (talk) 17:53, 4 May 2011 (UTC)
replies: text: You probably want to say "self-evident", then.Eregli bob (talk) 04:39, 18 June 2012 (UTC)
thread_title: Erf is "evidently" odd

message: What happen if the the limits of error function changes from -α to x.
::\frac{2}{\sqrt{\pi}}\int_a^x e^{-t^2} dt = \frac{2}{\sqrt{\pi}}\int_0^x e^{-t^2} dt - \frac{2}{\sqrt{\pi}}\int_0^a e^{-t^2} dt = \operatorname{erf}(x) - \operatorname{erf}(a)
:-lethe talk 16:11, 24 December 2005 (UTC)
thread_title:  If limits of error function changes? 

message: Shouldn’t the lower subscript of the integral be negative infinity instead of 0? The picture implies it.
Fvanris 14:06, 30 January 2006 (UTC)
replies: text: I don't think so. The picture implies that the value at zero is zero, so then the limit of integration has to be 0, not -infinity, no? Oleg Alexandrov (talk) 05:05, 31 January 2006 (UTC)
thread_title:  Subscript? 

message: Does anyone know why it is called the error function?  Is there something about it that I'm missing? —The preceding unsigned comment was added by 70.113.95.143 (talk • contribs).
:I'd be very interested to learn the answer for this.
::I'm not sure and I can't reference it, but I think the reason is that it is often useful to represent the probability of error in communication systems. The most common way to model noise is by a Gaussian distribution so, in order to calculate the probability of an error, you have to integrate the Gaussian function, thus getting expressions in terms of the error function. Some examples here in Wikipedia are Phase-shift keying, Amplitude-shift keying and Quadrature amplitude modulation. Alessio Damato 10:53, 22 February 2007 (UTC)
replies: text: Well, I don't have a refernce for you, but the article mentions that erf(\frac{a}{\sigma\sqrt{2}}) is the probability of a gaussian generated value to be within the range of +-a of the mean, doesn't it? So for a given error a, it gives you the likelyhood of that error.  —Preceding unsigned comment added by 87.174.73.108 (talk) 23:47, 11 March 2008 (UTC)
thread_title: Why?

message: Should approximations for the error function be mentioned? 
for example, one I saw on the web is 
:\mbox{erf}(x)^2 = 1-e^{-x^2\frac{4/\pi+ax^2}{1+ax^2}}
where \mbox{a} = \frac{-8}{3\pi}\frac{\pi-3}{\pi-4}
By the way, how do I use latex on these pages?Hiiiiiiiiiiiiiiiiiiiii 02:16, 9 July 2007 (UTC)
replies: text: Just the way you see it done.  Click on "edit this page" and you'll see it. Michael Hardy 03:50, 9 July 2007 (UTC)
replies: text:  I should add that although "displayed" TeX looks very good on Wikipedia, inline TeX often gets misaligned or looks much bigger than the surrounding text, and is therefore often avoided. Michael Hardy 03:51, 9 July 2007 (UTC)

text: 1-\exp\left(-x^2\frac{4/\pi+ax^2}{1+ax^2}\right)
instead of trying to fit that big fraction into a superscript. Michael Hardy 19:14, 9 July 2007 (UTC)

text: The formula looks cool, but how good is it? Can we add an error term (O(\cdot) or so)? Obviously, it is valid only for large positive x, but this is not said in the text. Wouldn't it be good to add a reference?  —Preceding unsigned comment added by 80.121.27.224 (talk) 17:39, 3 November 2007 (UTC)

text: The second sentence used to say 0.147, but someone incorrectly changed it (not realizing that it was intentionally different from the expression whose value is near 0.140012).  I've rewritten both sentences to reflect what the reference says.  Joule36e5 (talk) 09:55, 31 March 2011 (UTC)

text: This last approximation clearly does not work "over the complete range of values" and adds nothing useful to the article - I shall delete it. --catslash (talk) 23:40, 12 February 2018 (UTC)
thread_title: Approximation?

message: I'm studying and I really had a problem with this function. When I learned lesson from subject "Basis of telecommunications and data transfers" we used that function in some analyzing. In my notes stand similar function called error function but differing in product 1/sqrt(pi), and integrating borders were from minus infinity to x. I tried to make analysis with such function and failed. I turned to Internet I find form like one on Wikipedia. (I used that form and successfully made analyze) Nowhere professor's form. I gone to him and tell him, but he is refusing. I realized that there are diverse forms of this function. Then I look to some paper literature of base subject and really find professor's definition and similar ones. So if someone else find those variants also we can add them to article in separate section to avoid confusing others who can be in similar situation as I am. 
User:Vanished user 8ij3r8jwefi 19:25, 2 October 2007 (UTC)
thread_title: On alternate forms of error function for improving article

message: I've recently come across some references to a function ierfc in Crank (1975, the mathematics of diffusion).  I couldn't find anything on ierfc in Wolfram/Mathematica, but I found a few odd references, including in Abramovitz and Stegun.  Apparently ierfc is the integral of the erfc.
The easy formula for ierfc is
ierfc(x) = [exp(-x2)/sqrt(pi)] - x erfc(x)
   (sorry, I don't know LaTex).
I don't think there should be an additional article, but I suggest that (1) searches for ierfc be directed here, and (2) there be a brief mention of ierfc and its definition.
129.186.185.139 14:16, 17 October 2007 (UTC)
replies: text: The error function is not used for to describe the mathematics of diffusion, at least not for the type of diffusion that is normally referred to. Erf correctly describes the  distribution of the velocity of air (or another fluid) blowing from a hole, solving exactly the equations of Navier Stokes for that type of problem; however, that's not the diffusion process it is normally referred as in the diffusion of innovation, the diffusion of fashion and similar processes. These processes are described by the logistic function, which looks similar but is a different function. See diffusion of innovation. I'm going to eliminate the language referring to diffusion from the lede.--Gciriani (talk) 14:36, 29 April 2020 (UTC)
thread_title:  ierfc: Integral of the error function complement 

message: Maybe be an obvious Q, but what does 't' represent in the definition of erf(x)  —Preceding unsigned comment added by 88.110.201.64 (talk) 03:55, 22 October 2007 (UTC)
replies: text: It is the variable of integration, sometimes called a dummy variable as it doesn't actually represent a quantity. See the Integral article for details. Blair - Speak to me 03:38, 30 October 2007 (UTC)

text: Thanks for that link - it explains the concept much better than I could ever hope to! Blair - Speak to me 05:53, 30 October 2007 (UTC)
thread_title:  confused 

message: In the definition of the error function, perhaps it should be made clear that it applies to the integral of a normal distribution, i.e. a normalised Gaussian function. It is defined more clearly here (http://mathworld.wolfram.com/Erf.html). I'm not a mathematician, but I'm guessing the error function and all its approximations would not work if your integrand was not normalised.
Dieode 10:18, 29 October 2007 (UTC)
thread_title:  Integral of a normal distrubution 

message: Shouldn't "The error function at infinity is exactly 1" be stated as the limit as the error function approaches infinity is 1?  —Preceding unsigned comment added by 65.184.155.154 (talk) 19:36, 4 December 2007 (UTC)
thread_title:  Limits of the error function 

message: Would it perhaps be relevant in the applications section to mention that the error function pops up in the moment generating function for the Rayleigh distribution, which is the distribution of the magnitude of a twodimensional vector whose components are uncorrelated and each has a Gaussian distribution with identical variances. Relevant for, e.g., the statistical descrip of wind speed? -- Slaunger (talk) 11:55, 27 February 2008 (UTC)
thread_title:  Relation to [[moment generating function]] for the [[Rayleigh distribution]] 

message: The article claims that erf/erfc exist in GNU libc, but aren't part of any standard. I've come across references that claimed erf/erfc are part of the C99 ISO standard.  —Preceding unsigned comment added by 87.174.73.108 (talk) 23:43, 11 March 2008 (UTC)
replies: text: Yes, indeed they are functions in <math.h> in C99.  Oli Filth(talk) 00:17, 9 April 2008 (UTC)
thread_title:  Part of C99 standard? 

message: No approximation is listed for the inverse of erfc, I suggest at least including erfcinv(z)=erfinv(1-z), though it seems a bit trivial.  —Preceding unsigned comment added by 201.174.192.4 (talk) 18:02, 31 March 2008 (UTC)
thread_title:  Inverse erfc? 

message: How many arguments does Gamma function have in the representation of erf sugested?
Once it appear with single argument, then, with two argumetns.
In the definition, it appears with single argument. How to correct this? dima (talk) 04:14, 14 July 2008 (UTC)
thread_title:  representation through Gamma funciton 

message: A minor error is that, as raised in the above section, it mixed the gamma function, which takes one argument, and incomplete gamma function, which takes two arguments. Although we can think the ordinary gamma function as incomplete gamma function with scale=1, it should be mentioned somehow.
Moreover, another obvious major problem is that this expression is not correct, in that, simply in the formula, (x^n)^{-1/n}=1/x and  x(x^n)^{-1/n}=1. It seems not true. But I have on way to find the correct formula. Please...
193.10.97.31 (talk) 16:16, 3 December 2008 (UTC)
thread_title:  Some errors in the Gamma function expression of the generalised error functions 

message: Is the error function just a convolution of a step function (-1 : x<0, 0 : x==0, 1 : x > 0) with a Gaussian kernel? Numerically that looks right. It also makes sense in that erf is the integral of a Gaussian and convolution with a step gives you integration. If so, that should be mentioned, because it's a very easy way to think about erf. —Ben FrantzDale (talk) 05:30, 1 August 2009 (UTC)
thread_title:  Convolved step? 

message: i agree with Michael Hardy. this Approximation is crap. the error for x=3.5 is about 0.345!!!!!
someone find a better one?  —Preceding unsigned comment added by 46.116.223.100 (talk) 17:28, 5 March 2011 (UTC)
replies: text: I don't have anything off-hand, but I'd check out this section for any hints, in particular to Hart (1968) (I don't have any access to it) and West (2009). +mt 19:58, 29 March 2011 (UTC)
thread_title:  Approximation with elementary functions 

message: Should we add a note to the section Asymptotic Expansion that "!!" is the double factorial and not the factorial of the factorial? RJFJR (talk) 16:50, 7 February 2012 (UTC)
thread_title:  Double factorial 

message: The section labelled "The name 'error function'" does not actually ellaborate on the origin of the name. It instead provides details of the function's general use. This section should be rewritten to reflect its title and purpose. Monsieurisle (talk) 18:53, 12 February 2016 (UTC)
thread_title:  "The name 'error function'" 

message: I've removed the "Implementations" section.  There's no benefit to it, and it could potentially contain dozens more entries with no way to really delineate what belongs and what doesn't.  I'm including the removed text here just in case.  Deacon Vorbis (talk) 15:01, 17 September 2017 (UTC)
replies: text: I agree that most of these are trivial wrappers that aren't worth mentioning. But why not discuss the C implementations in the article? -- Nsda (talk) 11:44, 19 September 2017 (UTC)
thread_title:  Implementations 

message: Currently, the complementary error function Erfc is defined in 5.1, but the symbol Erfc appears first in 3.4 (then 3.xx, and 4.x). It would make sense to define it much earlier, possibly in the preamble.  — Preceding unsigned comment added by Ceacy (talk • contribs) 21:08, 19 November 2018 (UTC)
replies: text: Yeah, defining it first before it's used elsewhere would definitely be preferable.  I don't think it needs to be in the very lead, but something as simple as moving the related functions section near the beginning (I'd say after "name", but before "applications", but after applications wouldn't be terrible either).  –Deacon Vorbis (carbon • videos) 00:31, 20 November 2018 (UTC)

text: Well, I noticed the same thing and tried to fix this the other day, and then Deacon Vorbis objected to putting a brief definition in the lede. I still think it should be there. As it is after his edit, the article still talks about erfc before telling the reader what it is! Eric Kvaalen (talk) 16:07, 22 January 2019 (UTC)
replies: text: Hmm, oops then.  I'm a little busy, but I'll take another look at it when I get a chance.  –Deacon Vorbis (carbon • videos) 16:43, 22 January 2019 (UTC)
thread_title:  Reorganization? 

message: This seems more like a B-class article to me.  It has just about everything you need to know about the error function.  Bubba73 You talkin' to me? 20:48, 16 February 2019 (UTC)
thread_title:  C class or B class? 

message: Please check https://en.wikipedia.org/wiki/Wikipedia:Content_assessment#Quality_scale
Specifically, cleanup is necessary, there is substantial irrelevant material that would be better included by links to other wikipedia pages, and clarity of presentation, citations, and caveats concerning applicability leave much to be desired.
216.251.133.187 (talk) 00:34, 6 March 2019 (UTC)
thread_title: I Disagree

message: Can someone please expand the term
:\int_{0}^x e^{-t^2} dt
in the definition?  I came here to find out what the error function was because I'm trying to figure out how to integrate
:e^{-x^2}
and elsewhere I read that the error function was the way to do this.  Now I come here and I find I need to do the integration before I can calculate the error function.  How does this work?
—VeryRarelyStable (talk) 02:26, 22 May 2019 (UTC)
replies: text: See Nonelementary integral. Boris Tsirelson (talk) 03:51, 22 May 2019 (UTC)
thread_title:  How do you integrate e^(-x^2)?