Complementary Error Function Table Of Values
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the error function is a special function (non-elementary) of sigmoid shape which occurs in probability, statistics and partial complementary error function mathematica differential equations. It is also called the Gauss error function or probability integral. The error function is defined as: 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.
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
Complementary Error Function Ti 89
2 d t = 2 π ∫ 0 x e − t 2 erfc function table d t . {\displaystyle {\begin − 5\operatorname − 4 (x)&={\frac − 3{\sqrt {\pi }}}\int _{-x}^ − 2e^{-t^ − 1}\,\mathrm
Complimentary Error Function
− 0 t\\&={\frac 9{\sqrt {\pi }}}\int _ 8^ 7e^{-t^ 6}\,\mathrm 5 t.\end 4}} The complementary error function, denoted erfc, is defined as erfc ( x http://www.miniwebtool.com/error-function-calculator/ ) = 1 − erf ( x ) = 2 π ∫ x ∞ e − t 2 d t = e − x 2 erfcx ( x ) , {\displaystyle {\begin 1\operatorname 0 (x)&=1-\operatorname Φ 9 (x)\\&={\frac Φ 8{\sqrt {\pi }}}\int _ Φ 7^{\infty }e^{-t^ Φ 6}\,\mathrm Φ 5 t\\&=e^{-x^ Φ 4}\operatorname Φ 3 (x),\end Φ 2}} which also https://en.wikipedia.org/wiki/Error_function defines erfcx, the scaled complementary error function[3] (which can be used instead of erfc to avoid arithmetic underflow[3][4]). Another form of erfc ( x ) {\displaystyle \operatorname 1 (x)} for non-negative x {\displaystyle x} is known as Craig's formula:[5] erfc ( x | x ≥ 0 ) = 2 π ∫ 0 π / 2 exp ( − x 2 sin 2 θ ) d θ . {\displaystyle \operatorname Φ 9 (x|x\geq 0)={\frac Φ 8{\pi }}\int _ Φ 7^{\pi /2}\exp \left(-{\frac Φ 6}{\sin ^ Φ 5\theta }}\right)d\theta \,.} The imaginary error function, denoted erfi, is defined as erfi ( x ) = − i erf ( i x ) = 2 π ∫ 0 x e t 2 d t = 2 π e x 2 D ( x ) , {\displaystyle {\begin − 9\operatorname − 8 (x)&=-i\operatorname − 7 (ix)\\&={\frac − 6{\sqrt {\pi }}}\int _ − 5^ − 4e^ − 3}\,\mathrm − 2 t\\&={\frac − 1{\sqrt {\pi }}}e^ − 0}D(x),\end − 9}} where D(x) is the Dawson function (which can be used instead of erfi to avoid arithmetic overflow[3]). Despite the name "imagin
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