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function of a given number. Complementary Error Function In mathematics, the complementary error function (also tabulation of error function values 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)0.00.01.00.010.0112834160.9887165840.020.0225645750.9774354250.030.0338412220.9661587780.040.0451111060.9548888940.050.0563719780.9436280220.060.0676215940.9323784060.070.078857720.921142280.080.0900781260.9099218740.090.1012805940.8987194060.10.1124629160.8875370840.110.1236228960.8763771040.120.1347583520.8652416480.130.1458671150.8541328850.140.1569470330.8430529670.150.1679959710.8320040290.160.1790118130.8209881870.170.1899924610.8100075390.180.2009358390.7990641610.190.2118398920.7881601080.20.2227025890.7772974110.210.2335219230.7664780770.220.2442959120.7557040880.230.25502260.74497740.240.2657000590.7342999410.250.276326390.723673610.260.2868997230.7131002770.270.2974182190.7025817810.280.3078800680.6921199320.290.3182834960.6817165040.30.3286267590.6713732410.310.338908150.661091850.320.3491259950.6508740050.330.3592786550.6407213450.340.3693645290.6306354710.350.3793820540.6206179460.360.3893297010.6106702990.370.3992059840.6007940160.380.4090094530.5909905470.390.41873870.58126130.40.4283923550.5716076450.410.437969090.562030910.420.4474676180.5525323820.430.4568866950.5431133050.440.4662251150.5337748850.450.475481720.524518280.460.484655390.515344610.470.4937450510.5062549490.480.5027496710.4972503290.490.5116682610.4883317390.50.5204998780.4795001220.510.529243620.470756380.520.537898630.462101370.530.5464640970.4535359030.540.554939250.445060750.550.5633233660.4366766340.560.5716157640.4283842360.570.5798158060.4201841940.580.58792290.41207710.590.5959364970.4040635030.60.6038560910.3961439090.610.6116812190.3883187810.620.6194114620.3805885380.630.6270464430.3729535570.640.6345858290.3654141710.650.6420293270.3579706730.660.6493766880.3506233120.670.6566277020.3433722980.680.6637822030.3362177970.690.6708400620.3291599380.70.6778011940.3221988060.710.684665550.315334450.720.6914331230.3085668770.730.6981039430.3018960570.740.7046780780.2953219220.750.7111556340.2888443660.760.7175367530.2824632470.770.7238216140.2761783860.780.7300104310.2699895690.790.7361034540.2638965460.80.7421009650.2578990350.810.7480032810.2519967190.820.7538107510.2461892490.830.7595237570.2404762430.840.7651427110.2348572890.850.7706680580.2293319420.860.7761002680.2238997320.870.7814398450.2185601550.880.7866873190.2133
that occurs in probability, statistics, and partial differential equations describing diffusion. It is defined as:[1][2] erf ( x ) = 1 π ∫ − x x e − t 2 d t = 2 π ∫ 0
How To Calculate Error Function In Casio Calculator
x e − t 2 d t . {\displaystyle {\begin − 1\operatorname − 0 q function and erfc (x)&={\frac 9{\sqrt {\pi }}}\int _{-x}^ 8e^{-t^ 7}\,\mathrm 6 t\\&={\frac 5{\sqrt {\pi }}}\int _ 4^ how to find erf in scientific calculator 3e^{-t^ 2}\,\mathrm 1 t.\end 0}} In statistics, for nonnegative values of x, the error function has the following interpretation: for a random variable X that is normally distributed with mean 0 and variance http://www.miniwebtool.com/complementary-error-function-calculator/ 1 2 {\textstyle {\frac − 7 − 6}} , erf(x) describes the probability of X falling in the range [-x, x]. Contents 1 The name 'error function' 2 Derived and related functions 2.1 Complementary error function 2.2 Imaginary error function 2.3 Cumulative distribution function 3 Properties 3.1 Taylor series 3.2 Derivative and integral 3.3 Bürmann series 3.4 Inverse functions 3.5 Asymptotic expansion 3.6 Continued fraction expansion 3.7 Integral of error function with https://en.wikipedia.org/wiki/Error_function Gaussian density function 4 Approximation with elementary functions 5 Numerical approximations 6 Applications 7 Related functions 7.1 Generalized error functions 7.2 Iterated integrals of the complementary error function 8 Implementations 9 See also 9.1 Related functions 9.2 In probability 10 References 11 Further reading 12 External links The name 'error function'[edit] The error function is used in measurement theory (using probability and statistics), and its use in other branches of mathematics is typically unrelated to the characterization of measurement errors. In statistics, it is common to have a variable Y {\displaystyle Y} and its unbiased estimator Y ^ {\displaystyle {\hat − 3}} . The error is then defined as ε = Y ^ − Y {\displaystyle \varepsilon ={\hat − 1}-Y} . This makes the error a normally distributed random variable with mean 0 (because the estimator is unbiased) and some variance σ 2 {\displaystyle \sigma ^ − 9} ; this is written as ε ∼ N ( 0 , σ 2 ) {\textstyle \varepsilon \sim {\mathcal − 7}(0,\,\sigma ^ − 6)} . For the case where σ 2 = 1 2 {\textstyle \sigma ^ − 3={\frac − 2 − 1}} , i.e. an unbiased error variable ε ∼ N ( 0 , 1 2 ) {\textstyle \varepsilon \sim {\mathcal Φ 7}(0,\,{\frac Φ
Function Calculator Erf(x) Error Function Calculator erf(x) x = Form accepts both decimals and fractions. The error function, denoted erf, is defined http://www.had2know.com/academics/error-function-calculator-erf.html by the integral erf(x) = (2/√π)∫xo e-t2 dt. Erf(x) is closely related to the normal probability curve; the cumulative distribution function of a normally distributed random variable X is CDF(X) = 0.5 + 0.5erf[(X-)/σ√2], where is the mean and σ is the standard deviation of the distribution. The error function error function integral cannot be evaluated in terms of elemetary function, so one must use numerical algorithms. The error function is an odd function whose limit is -1 for negative values of x, and 1 for positive values of x. The function rapidly converges to its asympotic values; erf(3) = 0.99998 and erf(-3) error function table = -0.99998. Properties and Equations The values of x for which x = erf(x) are approximately 0.6175 and -0.6175. If you don't have access to an error function calculator such as the one above, you can approximate the function with the formula The error function can also be expressed with infinite series and continued fractions: You can approximate the inverse of the error function, erf-1(x), by inverting the approximation formula above. The inverse of erf has several interesting derivative and integral properties. © Had2Know 2010 How to Find the Great Circle Distance Between Two Points on a Sphere Gamma & Log Gamma Function Calculator Beta Function Calculator Weibull Distribution Calculator Digamma Function Calculator How to Test Whether Data is Normally Distributed How to Compute Normal Distribution Probabilities How to Read a Z-Score Table to Compute Probability Terms of Use | Privacy Policy | Contact Site Design by E. Emerson © 2010