ExamplesExamplesopen allclose all Basic Examples(3)Basic Examples(3) Evaluate numerically: In[1]:= Out[1]= In[1]:= Out[1]= In[1]:= Out[1]= Scope(6)Scope(6) Generalizations & Extensions(2)Generalizations & Extensions(2) Applications(3)Applications(3) Properties & Relations(7)Properties & Relations(7) Possible Issues(3)Possible Issues(3) Neat Examples(1)Neat Somewhat Generalized Mean Value Theorem Why does the material for space elevators have to be really strong? Princeton, NJ: Princeton University Press, p.105, 2003. Wolfram Cloud Central infrastructure for Wolfram's cloud products & services.

ExamplesExamplesopen allclose all Basic Examples(3)Basic Examples(3) Evaluate numerically: In[1]:= Out[1]= In[1]:= Out[1]= In[1]:= Out[1]= Scope(6)Scope(6) Generalizations & Extensions(3)Generalizations & Extensions(3) Applications(2)Applications(2) Properties & Relations(7)Properties & Relations(7) Possible Issues(3)Possible Issues(3) Neat Examples(1)Neat This series diverges for every finite x, and its meaning as asymptotic expansion is that, for any N ∈ N {\displaystyle N\in \mathbb Γ 2 } one has erfc ( Math. M.; Petersen, Vigdis B.; Verdonk, Brigitte; Waadeland, Haakon; Jones, William B. (2008).

Wolfram Data Framework Semantic framework for real-world data. 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. In order of increasing accuracy, they are: erf ( x ) ≈ 1 − 1 ( 1 + a 1 x + a 2 x 2 + a 3 x The pairs of functions {erff(),erfcf()} and {erfl(),erfcl()} take and return values of type float and long double respectively.

Computable Document Format Computation-powered interactive documents. It is implemented in the Wolfram Language as Erfi[z]. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W., NIST Handbook of Mathematical Functions, Cambridge University Press, ISBN978-0521192255, MR2723248 External links[edit] MathWorld – Erf Authority control NDL: 00562553 Retrieved from This allows one to choose the fastest approximation suitable for a given application.

Can Communism become a stable economic strategy? For , may be computed from (9) (10) (OEIS A000079 and A001147; Acton 1990). All rights reserved. Asymptotic expansion[edit] A useful asymptotic expansion of the complementary error function (and therefore also of the error function) for large real x is erfc ( x ) = e −

More complicated integrals include (31) (M.R.D'Orsogna, pers. The system returned: (22) Invalid argument The remote host or network may be down. Project going on longer than expected - how to bring it up to client? Press, William H.; Teukolsky, Saul A.; Vetterling, William T.; Flannery, Brian P. (2007), "Section 6.2.

While the mark is used herein with the limited permission of Wolfram Research, Stack Exchange and this site disclaim all affiliation therewith. W. Perl: erf (for real arguments, using Cody's algorithm[20]) is implemented in the Perl module Math::SpecFun Python: Included since version 2.7 as math.erf() and math.erfc() for real arguments. Incomplete Gamma Function and Error Function", Numerical Recipes: The Art of Scientific Computing (3rd ed.), New York: Cambridge University Press, ISBN978-0-521-88068-8 Temme, Nico M. (2010), "Error Functions, Dawson's and Fresnel Integrals",

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, The integrand ƒ=exp(−z2) and ƒ=erf(z) are shown in the complex z-plane in figures 2 and 3. It is defined as:[1][2] erf ( x ) = 1 π ∫ − x x e − t 2 d t = 2 π ∫ 0 x e − t Explicit numerical values are given only for real values of s between and .

For certain special arguments, Erf automatically evaluates to exact values. This usage is similar to the Q-function, which in fact can be written in terms of the error function. 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 Going to be away for 4 months, should we turn off the refrigerator or leave it on with water inside?

Company News Events About Wolfram Careers Contact Connect Wolfram Community Wolfram Blog Newsletter © 2016 Wolfram. Not the answer you're looking for? Here is a basic example of the form I am describing. (By the way, I am rewriting your metric function to properly localize x.) data = RandomReal[10, {4, 1000}]; metric[data_, perc_] Erf automatically threads over lists.

However, I should caution that the x-axis labeling is incorrect. Education All Solutions for Education Web & Software Authoring & Publishing Interface Development Software Engineering Web Development Finance, Statistics & Business Analysis Actuarial Sciences Bioinformatics Data Science Econometrics Financial Risk Management asked 2 years ago viewed 265 times active 1 year ago 10 votes · comment · stats Get the weekly newsletter! Browse other questions tagged special-functions arbitrary-precision or ask your own question.

Continued Fractions. Yes, it runs faster but at the expense of losing all the granularity when the function changes rapidly (which it does in the early part of this specific metric). Havil, J. Supancic, "On Bürmann's Theorem and Its Application to Problems of Linear and Nonlinear Heat Transfer and Diffusion," The Mathematica Journal, 2014.

Why did it take 10,000 years to discover the Bajoran wormhole? LCCN64-60036. Given random variable X ∼ Norm [ μ , σ ] {\displaystyle X\sim \operatorname {Norm} [\mu ,\sigma ]} and constant L < μ {\displaystyle L<\mu } : Pr [ X 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

Legal Site Map WolframAlpha.com WolframCloud.com Enable JavaScript to interact with content and submit forms on Wolfram websites. Is it "eĉ ne" or "ne eĉ"? Products & Services Mathematica Mathematica Online Development Platform Programming Lab Data Science Platform Finance Platform SystemModeler Enterprise Private Cloud Enterprise Mathematica Wolfram|Alpha Appliance Enterprise Solutions Corporate Consulting Technical Services Wolfram|Alpha Business Should I instead rely on NIntegrate and specify directly there my precision?

Wolfram Education Portal» Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. Wolfram Engine Software engine implementing the Wolfram Language. Solve and naming variables more hot questions question feed lang-mma about us tour help blog chat data legal privacy policy work here advertising info mobile contact us feedback Technology Life / Nevertheless I added another method to my post that may be closer to what you desire, and hopefully it also illustrates the cause of the problem in the first place. –Mr.Wizard♦

Related 25Global precision setting2Manipulating an arbitrary-precision ContourPlot4Can some one explain perplexing behavior of arbitrary precision arithmetic?5Accurately evaluating the hypergeometric function21Elegant high precision `log1p`?23Arbitrary precision spline interpolation6Multidimensional arbitrary precision spline interpolation on Name (optional) Email address (optional) Send Feedback Products Mathematica Mathematica Online Development Platform Programming Lab Data Science Platform Wolfram|Alpha Pro Mobile Apps Finance Platform SystemModeler Wolfram Workbench CDF Player Volume &