Error Function Complement
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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 x e − t 2 d t . {\displaystyle {\begin − error function values 6\operatorname − 5 (x)&={\frac − 4{\sqrt {\pi }}}\int _{-x}^ − 3e^{-t^ − 2}\,\mathrm − 1 t\\&={\frac error function equation − 0{\sqrt {\pi }}}\int _ 9^ 8e^{-t^ 7}\,\mathrm 6 t.\end 5}} The complementary error function, denoted erfc, is defined as derivative of error function erfc ( x ) = 1 − erf ( x ) = 2 π ∫ x ∞ e − t 2 d t = e − x 2 erfcx ( x ) , {\displaystyle {\begin 2\operatorname 1 error function integral (x)&=1-\operatorname 0 (x)\\&={\frac Φ 9{\sqrt {\pi }}}\int _ Φ 8^{\infty }e^{-t^ Φ 7}\,\mathrm Φ 6 t\\&=e^{-x^ Φ 5}\operatorname Φ 4 (x),\end Φ 3}} which also 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 2 (x)} for non-negative x {\displaystyle x} is known as Craig's formula:[5] erfc ( x | x ≥ 0 ) = 2 π ∫ 0 π /
How To Use Error Function
2 exp ( − x 2 sin 2 θ ) d θ . {\displaystyle \operatorname 0 (x|x\geq 0)={\frac Φ 9{\pi }}\int _ Φ 8^{\pi /2}\exp \left(-{\frac Φ 7}{\sin ^ Φ 6\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 Φ 0\operatorname − 9 (x)&=-i\operatorname − 8 (ix)\\&={\frac − 7{\sqrt {\pi }}}\int _ − 6^ − 5e^ − 4}\,\mathrm − 3 t\\&={\frac − 2{\sqrt {\pi }}}e^ − 1}D(x),\end − 0}} where D(x) is the Dawson function (which can be used instead of erfi to avoid arithmetic overflow[3]). Despite the name "imaginary error function", erfi ( x ) {\displaystyle \operatorname 8 (x)} is real when x is real. When the error function is evaluated for arbitrary complex arguments z, the resulting complex error function is usually discussed in scaled form as the Faddeeva function: w ( z ) = e − z 2 erfc ( − i z ) = erfcx ( − i z ) . {\displaystyle w(z)=e^{-z^ 6}\operatorname 5 (-iz)=\operatorname 4 (-iz).} Contents 1 The name "error function" 2 Properties 2.1 Taylor series 2.2 Derivative and integral 2.3 Bürmann series 2.4 Inverse functions 2.5 Asymptotic expansion 2.6 Continued fraction expansion 2.7 Integral of error function with
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How To Solve Error Function
Elementary Math Special Functions MATLAB Functions erfc On this page Syntax Description Examples erf(2) Find Complementary Error Function Find Bit Error Rate of Binary Phase-Shift Keying Avoid Roundoff Errors Using Complementary Error Function complementary error function Input Arguments x More About Complementary Error Function Tall Array Support Tips See Also This is machine translation Translated by Mouse over text to see original. Click the button below to https://en.wikipedia.org/wiki/Error_function 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 https://www.mathworks.com/help/matlab/ref/erfc.html 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) exampleDescriptionexampleerfc(x
) returns the Complementary Error Function evaluated for each element of x. Use the erfc function to replace 1 - erf(x) for greater accuracy when erf(x) is close to 1.Examplescollapse allFind Complementary Error FunctionOpen ScriptFind the complementary error function of a value.erfc(0.35) ans = 0.6206 Find the complementary error function of the elements of a vector.V = [-0.5 0 1 0.72]; erfc(V) ans = 1.5205 1.0000 0.1573 0.3086 Find the complementary error function of the elements of a matrix.M = [0.29 -0.11; 3.1 -2.9]; erfc(M) ans = 0.6817 1.1236 0.0000 2.0000 Find Bit Error Rate of Binary Phase-Shift KeyingOpen ScriptThe bit error rate (BER) of binary phase-shift keying (BPSK), assuming additive white gaussian noise (AWGN), is Plot the BER for BPSK for values of from 0dB to 10dB.EbN0_dB = 0:0.1:10; EbN0 = 10.^(EbN0_dB/10); BER = 1/2.*erfc(sqrt(EbN0)); semilogy(EbN0_dB,BER) grid on ylabel('BER') xlabel('E_b/N_0 (dB)') title('Bit Err
function of a given number. Complementary Error Function In mathematics, the complementary error function (also error function complement 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)0.00.01.00.010.0112834160.9887165840.020.0225645750.9774354250.030.0338412220.9661587780.040.0451111060.9548888940.050.0563719780.9436280220.060.0676215940.9323784060.070.078857720.921142280.080.0900781260.9099218740.090.1012805940.8987194060.10.1124629160.8875370840.110.1236228960.8763771040.120.1347583520.8652416480.130.1458671150.8541328850.140.1569470330.8430529670.150.1679959710.8320040290.160.1790118130.8209881870.170.1899924610.8100075390.180.2009358390.7990641610.190.2118398920.7881601080.20.2227025890.7772974110.210.2335219230.7664780770.220.2442959120.7557040880.230.25502260.74497740.240.2657000590.7342999410.250.276326390.723673610.260.2868997230.7131002770.270.2974182190.7025817810.280.3078800680.6921199320.290.3182834960.6817165040.30.3286267590.6713732410.310.338908150.661091850.320.3491259950.6508740050.330.3592786550.6407213450.340.3693645290.6306354710.350.3793820540.6206179460.360.3893297010.6106702990.370.3992059840.6007940160.380.4090094530.5909905470.390.41873870.58126130.40.4283923550.5716076450.410.437969090.562030910.420.4474676180.5525323820.430.4568866950.5431133050.440.4662251150.5337748850.450.475481720.524518280.460.484655390.515344610.470.4937450510.5062549490.480.5027496710.4972503290.490.5116682610.4883317390.50.5204998780.4795001220.510.529243620.470756380.520.537898630.462101370.530.5464640970.4535359030.540.554939250.445060750.550.5633233660.4366766340.560.5716157640.4283842360.570.5798158060.42018
ChapterAn Atlas of Functions pp 405-415 Date: 30 September 2008The Error Function erf(x) and Its Complement erfc(x)Keith B. OldhamAffiliated withTrent University Email author , Jan C. MylandAffiliated withTrent University, Jerome SpanierAffiliated withUniversity of California at Irvine Buy this eBook * Final gross prices may vary according to local VAT. Get Access Page %P Close Plain text Look Inside Chapter Metrics Provided by Bookmetrix Reference tools Export citation EndNote (.ENW) JabRef (.BIB) Mendeley (.BIB) Papers (.RIS) Zotero (.RIS) BibTeX (.BIB) Add to Papers Other actions About this Book Reprints and Permissions Share Share this content on Facebook Share this content on Twitter Share this content on LinkedIn Supplementary Material (0) References (0) About this Chapter Title The Error Function erf(x) and Its Complement erfc(x) Book Title An Atlas of Functions Book Subtitle with Equator, the Atlas Function Calculator Pages pp 405-415 Copyright 2009 DOI 10.1007/978-0-387-48807-3_41 Print ISBN 978-0-387-48806-6 Online ISBN 978-0-387-48807-3 Publisher Springer US Copyright Holder Springer Science+Business Media, LLC Additional Links About this Book Topics Applications of Mathematics Special Functions Real Functions Theoretical, Mathematical and Computational Physics Computational Intelligence Industry Sectors Pharma Materials & Steel Biotechnology Electronics Aerospace Oil, Gas & Geosciences Engineering eBook Packages Mathematics and Statistics Authors Keith B. Oldham (1) Jan C. Myland (1) Jerome Spanier (2) Author Affiliations 1. Trent University, Peterborough, Ontario K9J 7B8, Canada 2. University of California at Irvine, Irvine, CA 92697, USA Continue reading... To view the rest of this content please follow the download PDF link above. We use cookies to improve your experience with our site. More information Accept Over 10 million scientific documents at your fingertips Browse by Discipline Architecture & Design Astronomy Biomedical Sciences Business & Management Chemistry Computer Science Earth Sciences & Geography Economics Education & Language Energy Engineering Environmental Sciences Food Science & Nutrition Law Life Sciences Materials Mathematics Medicine Philosophy Physics Psychology Public Health Social Sciences Statistics Our Content Journals Books Book Series Protocols Reference Works Other Sites Springer.com SpringerProtocols SpringerMaterials AdisInsight Help & Contacts Contact Us Impressum Legal © Springer International Publishing