How To Solve Error Function
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Random Entry New in MathWorld MathWorld Classroom About MathWorld Contribute to MathWorld Send a Message to the Team MathWorld Book Wolfram Web Resources» 13,594 entries Last updated: Tue Sep 27 2016 Created, developed, and error function calculator nurturedbyEricWeisstein at WolframResearch Calculus and Analysis>Special Functions>Erf> Calculus and Analysis>Complex Analysis>Entire Functions> complementary error function Interactive Entries>webMathematica Examples> More... History and Terminology>Wolfram Language Commands> MathWorld Contributors>D'Orsogna> Less... Erf is the "error function" encountered
Error Function Table
in integrating the normal distribution (which is a normalized form of the Gaussian function). It is an entire function defined by (1) Note that some authors (e.g., Whittaker and Watson
Error Function Matlab
1990, p.341) define without the leading factor of . Erf is implemented in the Wolfram Language as Erf[z]. A two-argument form giving is also implemented as Erf[z0, z1]. Erf satisfies the identities (2) (3) (4) where is erfc, the complementary error function, and is a confluent hypergeometric function of the first kind. For , (5) where is the incomplete gamma function. inverse error function Erf can also be defined as a Maclaurin series (6) (7) (OEIS A007680). Similarly, (8) (OEIS A103979 and A103980). For , may be computed from (9) (10) (OEIS A000079 and A001147; Acton 1990). For , (11) (12) Using integration by parts gives (13) (14) (15) (16) so (17) and continuing the procedure gives the asymptotic series (18) (19) (20) (OEIS A001147 and A000079). Erf has the values (21) (22) It is an odd function (23) and satisfies (24) Erf may be expressed in terms of a confluent hypergeometric function of the first kind as (25) (26) Its derivative is (27) where is a Hermite polynomial. The first derivative is (28) and the integral is (29) Min Max Re Im Erf can also be extended to the complex plane, as illustrated above. A simple integral involving erf that Wolfram Language cannot do is given by (30) (M.R.D'Orsogna, pers. comm., May 9, 2004). More complicated integrals include (31) (M.R.D'Orsogna, pers. comm., Dec.15, 2005). Erf has the continued fraction (32) (33) (Wall 1948, p.357), first stated by Laplace in 1805 and Leg
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Error Function Excel
Trial Software Product Updates Documentation Home MATLAB Examples Functions Release error function properties Notes PDF Documentation Mathematics Elementary Math Special Functions MATLAB Functions erf On this page Syntax error function python Description Examples Find Error Function Find Cumulative Distribution Function of Normal Distribution Calculate Solution of Heat Equation with Initial Condition Input Arguments x More http://mathworld.wolfram.com/Erf.html About Error Function Tall Array Support Tips See Also This is machine translation Translated by Mouse over text to see original. Click the button below to return to the English verison of the page. Back to English × Translate This Page Select Language Bulgarian Catalan Chinese Simplified Chinese Traditional https://www.mathworks.com/help/matlab/ref/erf.html Czech Danish Dutch English Estonian Finnish French German Greek Haitian Creole Hindi Hmong Daw Hungarian Indonesian Italian Japanese Korean Latvian Lithuanian Malay Maltese Norwegian Polish Portuguese Romanian Russian Slovak Slovenian Spanish Swedish Thai Turkish Ukrainian Vietnamese Welsh MathWorks Machine Translation The automated translation of this page is provided by a general purpose third party translator tool. MathWorks does not warrant, and disclaims all liability for, the accuracy, suitability, or fitness for purpose of the translation. Translate erfError functioncollapse all in page Syntaxerf(x) exampleDescriptionexampleerf(x
) returns the Error Function evaluated for each element of x.Examplescollapse allFind Error FunctionOpen ScriptFind the error function of a value.erf(0.76) ans = 0.7175 Find the error function of the elements of a vector.V = [-0.5 0 1 0.72]; erf(V) ans = -0.5205 0 0.8427 0.6914 Find the error function of the elements of a matrix.M = [0.29 -0.11; 3.1 -2.9]; e
here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company Business Learn more about hiring http://math.stackexchange.com/questions/38524/how-can-i-solve-this-equation-contains-error-function developers or posting ads with us Mathematics Questions Tags Users Badges Unanswered Ask Question _ Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top How can I solve this equation (contains error function)? up error function vote 1 down vote favorite Edited out incorrect formula Can someone please solve this equation for x? I have no idea what to do with the $\mathrm{erf}$ (error function). Edit: Hm, it did not work correctly... here is the function I meant to solve for x in symbolic form: $$f(x) = a*\left(0.5*\mathrm{erf}\left(\frac{x-b}{c\sqrt{2}}+.5\right)\right)+d$$ Coefficients (with 99% confidence bounds): a = 1.412 (1.411, 1.412) b = 1.259 (1.259, 1.259) c = 1.003 (1.002, 1.003) d = 0.3016 (0.3014, 0.3017) When how to solve I solve for f(x) with x=1 I get ans = 0.5460 I want to plug 0.5460 into a formula and get 1 back. Chris, this is the Finv function you spoke of in my other question. statistics special-functions share|cite|improve this question edited May 12 '11 at 0:42 J. M. 53k5118254 asked May 11 '11 at 18:46 Mike Furlender 11315 Your original had a missing parenthesis. Do check if my corrections are accurate. –J. M. May 11 '11 at 18:49 In any event, what computing environment are you using? If there is no implementation of the inverse error function, then you will have to use Newton-Raphson... –J. M. May 11 '11 at 18:50 @J.M Yeah your correction is correct. I am using MatLab, and there is an inverse error function (erfinv). I realize that erfinv(erf(x)) = x, but... I really suck at math :( –Mike Furlender May 11 '11 at 19:05 I am not MatLab user, but I suspect that it has a solve function for this kind of trivial manipulations. –Phira May 11 '11 at 21:03 @user9325 I don't think so; it said that it can't compute it. –Mike Furlender May 11 '11 at 21:44 | show 1 more comment 2 Answers 2 active oldest votes up vote 1 down vote accepted Let's start with the "general form" you say you had: $$a\left(\frac12\mathrm{erf}\left(\frac{
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