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# Complementary Error Function

## Contents

D: A D package[16] exists providing efficient and accurate implementations of complex error functions, along with Dawson, Faddeeva, and Voigt functions. Based on your location, we recommend that you select: . Integrals and Series, Vol.2: Special Functions. N ! ∫ x ∞ t − 2 N e − t 2 d t , {\displaystyle R_ − 7(x):={\frac {(-1)^ − 6}{\sqrt {\pi }}}2^ − 5{\frac {(2N)!} − 4}\int _ http://xhpcreations.com/error-function/complementary-error-function-table.html

H. 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, Web browsers do not support MATLAB commands. New York: Dover, 1972. https://www.mathworks.com/help/matlab/ref/erf.html

## Complementary Error Function

doi:10.3888/tmj.16–11.Schöpf, Supancic ^ E. See also Related functions Gaussian integral, over the whole real line Gaussian function, derivative Dawson function, renormalized imaginary error function Goodwin–Staton integral In probability Normal distribution Normal cumulative distribution function, a Wolfram Education Portal» Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. Close Was this topic helpful? × Select Your Country Choose your country to get translated content where available and see local events and offers.

Washington, DC: Hemisphere, pp.385-393, 1987. 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 Error Function Table Acknowledgments Trademarks Patents Terms of Use Deutschland Patente Handelsmarken Datenschutz Preventing Piracy © 1994-2016 The MathWorks, Inc.

Join the conversation MATLAB Function Reference Go to function: Search Help Desk erf, erfc, erfcx, erfinv Examples

Error functions Syntax Y = erf(X) Error function Y = erfc(X) Complementary error function Wolfram Language» Knowledge-based programming for everyone. Based on your location, we recommend that you select: . M.; Petersen, Vigdis B.; Verdonk, Brigitte; Waadeland, Haakon; Jones, William B. (2008).

Comp. 23 (107): 631–637. Erf(2/sqrt(2)) Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. Erf is the "error function" encountered in integrating the normal distribution (which is a normalized form of the Gaussian function). LCCN64-60036.

## Erfc Matlab

New York: Random House, 1963. Springer-Verlag. Complementary Error Function http://mathworld.wolfram.com/Erf.html Wolfram Web Resources Mathematica» The #1 tool for creating Demonstrations and anything technical. Inverse Error Function Excel: Microsoft Excel provides the erf, and the erfc functions, nonetheless both inverse functions are not in the current library.[17] Fortran: The Fortran 2008 standard provides the ERF, ERFC and ERFC_SCALED

MathWorks does not warrant, and disclaims all liability for, the accuracy, suitability, or fitness for purpose of the translation. weblink See Example 2.MuPAD can simplify expressions that contain error functions and their inverses. Negative integer values of Im(ƒ) are shown with thick red lines. The inverse imaginary error function is defined as erfi − 1 ⁡ ( x ) {\displaystyle \operatorname ∑ 8 ^{-1}(x)} .[10] For any real x, Newton's method can be used to Erf Function Calculator

Instead, replace erfinv(1-x) with erfcinv(x). Washington, DC: Math. These generalised functions can equivalently be expressed for x>0 using the Gamma function and incomplete Gamma function: E n ( x ) = 1 π Γ ( n ) ( Γ navigate here For real values x, the system applies the following simplification rules:inverf(erf(x)) = inverf(1 - erfc(x)) = inverfc(1 - erf(x)) = inverfc(erfc(x)) = xinverf(-erf(x)) = inverf(erfc(x) - 1) = inverfc(1 + erf(x))

R. (March 1, 2007), "On the calculation of the Voigt line profile: a single proper integral with a damped sine integrand", Monthly Notices of the Royal Astronomical Society, 375 (3): 1043–1048, Inverse Error Function Matlab When erf(x) is close to 1, then 1 - erf(x) is a small number and might be rounded down to 0. Related functions The error function is essentially identical to the standard normal cumulative distribution function, denoted Φ, also named norm(x) by software languages, as they differ only by scaling and translation.

## To use these approximations for negative x, use the fact that erf(x) is an odd function, so erf(x)=−erf(−x).

It is defined as:[1][2] erf ⁡ ( x ) = 1 π ∫ − x x e − t 2 d t = 2 π ∫ 0 x e − t Arfken, G. Intermediate levels of Im(ƒ)=constant are shown with thin green lines. Erf(1) For previous versions or for complex arguments, SciPy includes implementations of erf, erfc, erfi, and related functions for complex arguments in scipy.special.[21] A complex-argument erf is also in the arbitrary-precision arithmetic

The inverse error function is usually defined with domain (−1,1), and it is restricted to this domain in many computer algebra systems. A Course in Modern Analysis, 4th ed. Also has erfi for calculating i erf ⁡ ( i x ) {\displaystyle i\operatorname {erf} (ix)} Maple: Maple implements both erf and erfc for real and complex arguments. his comment is here Translate erfinvInverse error functioncollapse all in page Syntaxerfinv(x) exampleDescriptionexampleerfinv(x) returns the Inverse Error Function evaluated for each element of x.

and Stegun, I.A. (Eds.). "Error Function and Fresnel Integrals." Ch.7 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. Cambridge, England: Cambridge University Press, 1990. MR0167642.