Calculating Complementary Error Function
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function of a given number. Complementary Error Function In mathematics, the complementary error function (also complementary error function mathematica known as Gauss complementary error function) is defined as: Complementary Error Function Table The following is the error function and complementary error function table that shows the values of erf(x) and erfc(x) for x ranging from 0 to 3.5 with increment of 0.01. xerf(x)erfc(x)0.00.01.00.010.0112834160.9887165840.020.0225645750.9774354250.030.0338412220.9661587780.040.0451111060.9548888940.050.0563719780.9436280220.060.0676215940.9323784060.070.078857720.921142280.080.0900781260.9099218740.090.1012805940.8987194060.10.1124629160.8875370840.110.1236228960.8763771040.120.1347583520.8652416480.130.1458671150.8541328850.140.1569470330.8430529670.150.1679959710.8320040290.160.1790118130.8209881870.170.1899924610.8100075390.180.2009358390.7990641610.190.2118398920.7881601080.20.2227025890.7772974110.210.2335219230.7664780770.220.2442959120.7557040880.230.25502260.74497740.240.2657000590.7342999410.250.276326390.723673610.260.2868997230.7131002770.270.2974182190.7025817810.280.3078800680.6921199320.290.3182834960.6817165040.30.3286267590.6713732410.310.338908150.661091850.320.3491259950.6508740050.330.3592786550.6407213450.340.3693645290.6306354710.350.3793820540.6206179460.360.3893297010.6106702990.370.3992059840.6007940160.380.4090094530.5909905470.390.41873870.58126130.40.4283923550.5716076450.410.437969090.562030910.420.4474676180.5525323820.430.4568866950.5431133050.440.4662251150.5337748850.450.475481720.524518280.460.484655390.515344610.470.4937450510.5062549490.480.5027496710.4972503290.490.5116682610.4883317390.50.5204998780.4795001220.510.529243620.470756380.520.537898630.462101370.530.5464640970.4535359030.540.554939250.445060750.550.5633233660.4366766340.560.5716157640.4283842360.570.5798158060.4201841940.580.58792290.41207710.590.5959364970.4040635030.60.6038560910.3961439090.610.6116812190.3883187810.620.6194114620.3805885380.630.6270464430.3729535570.640.6345858290.3654141710.650.6420293270.3579706730.660.6493766880.3506233120.670.6566277020.3433722980.680.6637822030.3362177970.690.6708400620.3291599380.70.6778011940.3221988060.710.684665550.315334450.720.6914331230.3085668770.730.6981039430.3018960570.740.7046780780.2953219220.750.7111556340.2888443660.760.7175367530.2824632470.770.7238216140.2761783860.780.7300104310.2699895690.790.7361034540.2638965460.80.7421009650.2578990350.810.748
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Complementary Error Function Ti 89
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Complimentary Error Function
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 to accurately calculate the error function erf(x) with a computer? up vote http://www.miniwebtool.com/complementary-error-function-calculator/ 9 down vote favorite 2 I am looking for an accurate algorithm to calculate the error function I have tried using [this formula] (http://stackoverflow.com/a/457805) (Handbook of Mathematical Functions, formula 7.1.26), but the results are not accurate enough for the application. statistics algorithms numerical-methods special-functions share|cite|improve this question edited Jan 10 '14 at 4:47 pnuts 1056 asked Jul 20 '10 at 20:20 badp 6741225 You may want to take a look at python's code.google.com/p/mpmath or other libraries that advertise http://math.stackexchange.com/questions/97/how-to-accurately-calculate-the-error-function-erfx-with-a-computer a "multiple precision" feature. Also, this may be a better question for stack overflow instead, since it's more of a computer science thing. –Jon Bringhurst Jul 20 '10 at 20:26 @Jon: Nope, I'm not interested in a library, there is no such library for the language I'm writing in (yet). I need the mathematical algorithm. –badp Jul 20 '10 at 20:49 Have you tried numerical integration? Gaussian Quadrature is an accurate technique –Digital Gal Aug 28 '10 at 1:25 GQ is nice, but with (a number of) efficient methods for computing $\mathrm{erf}$ already known, I don't see the point. –J. M. Aug 29 '10 at 23:07 add a comment| 4 Answers 4 active oldest votes up vote 9 down vote accepted I am assuming that you need the error function only for real values. For complex arguments there are other approaches, more complicated than what I will be suggesting. If you're going the Taylor series route, the best series to use is formula 7.1.6 in Abramowitz and Stegun. It is not as prone to subtractive cancellation as the series derived from integrating the power series for $\exp(-x^2)$. This is good only for "small" arguments. For large arguments, you can use either the asymptotic series or the continued fraction representations. Otherwise, may I direct you to these papers by S. Winitzki that give nice approximations to the error function. (added on
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Error Function Free Statistics Calculators: Home > Complementary Error Function Calculator Complementary Error Function Calculator This calculator will compute the value of the complementary error function (i.e., the area under the error function from x to positive infinity), given the limit of integration x. The complementary error function is also known as the Gauss complementary error function.Please enter the necessary parameter values, and then click 'Calculate'. x: Related Resources Calculator Formulas References Related Calculators Search Free Statistics Calculators version 4.0 The Free Statistics Calculators index now contains 106 free statistics calculators! Copyright © 2006 - 2016 by Dr. Daniel Soper. All rights reserved.