Integration Error Function Matlab
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Erf(1/sqrt(2))
Examples Functions and Other Reference Release Notes PDF Documentation Mathematics Mathematical Functions Symbolic Math erfc matlab Toolbox Functions erfc On this page Syntax Description Examples Complementary Error Function for Floating-Point and Symbolic Numbers Error Function for Variables and Expressions Complementary erf(2/sqrt(2)) Error Function for Vectors and Matrices Special Values of Complementary Error Function Handling Expressions That Contain Complementary Error Function Plot Complementary Error Function Input Arguments X K More About Complementary Error Function Iterated Integral of Complementary Error Function Tips Algorithms References See Also This is machine translation Translated by
Inverse Error Function Matlab
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 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 erfcComplementary error functioncollapse all in page Syntaxerfc(X) exampleerfc(K,X) exampleDescriptionexampleerfc(X
) represents the complementary error function of X, that is,erfc(X) = 1 - erf(X).exampleerfc(K
,X) represents the iterated integral of the c
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Error Function Table
MATLAB Functions integral On this page Syntax Description Examples Improper Integral Parameterized Function Singularity at Lower Limit Complex Contour Integration Using Waypoints Vector-Valued Function https://www.mathworks.com/help/symbolic/erfc.html Improper Integral of Oscillatory Function Related Examples Input Arguments fun xmin xmax Name-Value Pair Arguments 'AbsTol' 'RelTol' 'ArrayValued' 'Waypoints' More About Tips References 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 https://www.mathworks.com/help/matlab/ref/integral.html the page. Back to English × Translate This Page Select Language Bulgarian Catalan Chinese Simplified Chinese Traditional 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 integralNumerical integrationcollapse all in page Syntaxq = integral(fun,xmin,xmax) exampleq = integral(fun,xmin,xmax,Name,Value) exampleDescriptionexampleq = integral(fun
,xmin,xmax) numerically integrates function fun from xmin to xmax using global adaptive quadrature and default error tolerances.exampleq = integral(fun
,xmin,xmax,Name,Value) specifies additional options with one or more Name,Value pair arguments. For example, spec
Support Support Newsreader MathWorks Search MathWorks.com MathWorks Newsreader Support MATLAB Newsgroup MATLAB Central Community Home MATLAB Answers File Exchange Cody Blogs Newsreader Link https://www.mathworks.com/matlabcentral/newsreader/view_thread/15809 Exchange ThingSpeak Anniversary Home Post A New Message Advanced Search Help MATLAB Central Community Home MATLAB Answers File Exchange Cody Blogs Newsreader Link Exchange ThingSpeak Anniversary Home Post A http://cens.ioc.ee/local/man/matlab/techdoc/ref/erf.html New Message Advanced Search Help Trial software Help: Integration of error function Subject: Help: Integration of error function From: Eungyu Park Date: 2 Apr, 2000 16:10:56 Message: 1 error function of 2 Reply to this message Add author to My Watch List View original format Flag as spam I have no idea how to integrate a, b arbitrary constant t variable(fixed) tau dummy int(erf(a/(t-tau)^(1/2))-erf(b/(t-tau)^(1/2)), tau, 0, t) If anybody has idea about that integration, please help me! Thank you Subject: Help: Integration of error function From: deboeck error function matlab Date: 3 Apr, 2000 15:06:13 Message: 2 of 2 Reply to this message Add author to My Watch List View original format Flag as spam This is a multi-part message in MIME format. --------------42D7F2598549D4A5D22178B4 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Hi Eungyu, Mathematica can solve this type of integrals, I found for int(erf(a/(t-tau)^(1/2)),tau,0,t) a rather complicated solution, but after some algebra : 2\,a\,\left( -a + \frac{{\sqrt{t}}} {e^{\frac{a^2}{t}}\,{\sqrt{\pi }}} \right) + \left( 2\,a^2 + t \right) \,\Mfunction{Erf}(\frac{a}{{\sqrt{t}}}) hope this helps regards, Bart Eungyu Park wrote: > I have no idea how to integrate > > a, b arbitrary constant > t variable(fixed) > tau dummy > > int(erf(a/(t-tau)^(1/2))-erf(b/(t-tau)^(1/2)), tau, 0, t) > > If anybody has idea about that integration, please help me! > > Thank you --------------42D7F2598549D4A5D22178B4 Content-Type: text/x-vcard; charset=us-ascii; name="deboeck.vcf" Content-Transfer-Encoding: 7bit Content-Description: Card for deboeck Content-Disposition: attachment; filename="deboeck.vcf" begin:vcard n:De Boeck;Bart tel;work:+32 (0)3 218.04.33 x-mozilla-html:FALSE org:University of Antwerp;Department of Physics adr:;;Groenenborgerlaan 171;2020 Antwerpen;;; version:2.1 email;internet:deboeck@ruca.ua.ac.be title:Research Student fn:Bart De Boeck end:vcard --------------42D7F2598549D4A5D22178B4-- Feed for this Thread Add to M
X = erfinv(Y) Inverse of the error function Definition The error function erf(X) is twice the integral of the Gaussian distribution with 0 mean and variance of:
The complementary error function erfc(X) is defined as: The scaled complementary error function erfcx(X) is defined as: For large X, erfcx(X) is approximately . Description Y = erf(X) returns the value of the error function for each element of real array X. Y = erfc(X) computes the value of the complementary error function. Y = erfcx(X) computes the value of the scaled complementary error function. X = erfinv(Y) returns the value of the inverse error function for each element of Y. The elements of Y must fall within the domain Examples erfinv(1) is Inf erfinv(-1) is -Inf. For abs(Y) > 1, erfinv(Y) is NaN. Remarks The relationship between the error function and the standard normal probability distribution is: x = -5:0.1:5; standard_normal_cdf = (1 + (erf(x/sqrt(2))))./2; Algorithms For the error functions, the MATLAB code is a translation of a Fortran program by W. J. Cody, Argonne National Laboratory, NETLIB/SPECFUN, March 19, 1990. The main computation evaluates near-minimax rational approximations from [1]. For the inverse of the error function, rational approximations accurate to approximately six significant digits are used to generate an initial approximation, which is then improved to full accuracy by two steps of Newton's method. The M-file is easily modified to eliminate the Newton improvement. The resulting code is about three times faster in execution, but is considerably less accurate. References [1] Cody, W. J., "Rational Chebyshev Approximations for the Error Function," Math. Comp., pgs. 631-638, 1969 [ Previous | Help Desk | Next ]