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Erf Function Calculator
developers or posting ads with us Mathematics Questions Tags Users Badges Unanswered Ask Question _ Mathematics Stack Exchange is a error function table question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask inverse error function a question Anybody can answer The best answers are voted up and rise to the top Why is the error function defined as it is? up vote 35 down vote favorite 6 $\newcommand{\erf}{\operatorname{erf}}$ This may be a very naïve question, but here goes. The error function $\erf$ is defined by $$\erf(x) = \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2}dt.$$ Of course, it is closely related to the normal cdf $$\Phi(x)
Error Function Matlab
= P(N < x) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^x e^{-t^2/2}dt$$ (where $N \sim N(0,1)$ is a standard normal) by the expression $\erf(x) = 2\Phi(x \sqrt{2})-1$. My question is: Why is it natural or useful to define $\erf$ normalized in this way? I may be biased: as a probabilist, I think much more naturally in terms of $\Phi$. However, anytime I want to compute something, I find that my calculator or math library only provides $\erf$, and I have to go check a textbook or Wikipedia to remember where all the $1$s and $2$s go. Being charitable, I have to assume that $\erf$ was invented for some reason other than to cause me annoyance, so I would like to know what it is. If nothing else, it might help me remember the definition. Wikipedia says: The standard normal cdf is used more often in probability and statistics, and the error function is used more often in other branches of mathematics. So perhaps a practitioner of one of these mysterious "other branches of mathematics" would care to enlighten me. The most reasonable expression I've found is that $$P(|N| < x) = \erf(x/\sqrt{2}).$$ This at least gets rid
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Error Function Python
History and Terminology>Wolfram Language Commands> MathWorld Contributors>D'Orsogna> Less... Erf is the "error function" encountered in integrating the normal distribution (which is a normalized form of http://math.stackexchange.com/questions/37889/why-is-the-error-function-defined-as-it-is the Gaussian function). It is an entire function defined by (1) Note that some authors (e.g., Whittaker and Watson 1990, p.341) define without the leading factor of . Erf is implemented in the Wolfram Language as Erf[z]. A two-argument form giving is also implemented as Erf[z0, z1]. Erf satisfies the identities http://mathworld.wolfram.com/Erf.html (2) (3) (4) where is erfc, the complementary error function, and is a confluent hypergeometric function of the first kind. For , (5) where is the incomplete gamma function. Erf can also be defined as a Maclaurin series (6) (7) (OEIS A007680). Similarly, (8) (OEIS A103979 and A103980). For , may be computed from (9) (10) (OEIS A000079 and A001147; Acton 1990). For , (11) (12) Using integration by parts gives (13) (14) (15) (16) so (17) and continuing the procedure gives the asymptotic series (18) (19) (20) (OEIS A001147 and A000079). Erf has the values (21) (22) It is an odd function (23) and satisfies (24) Erf may be expressed in terms of a confluent hypergeometric function of the first kind as (25) (26) Its derivative is (27) where is a Hermite polynomial. The first derivative is (28) and the integral is (29) Min Max Re Im Erf ca
in physics?UpdateCancelAnswer Wiki3 Answers Hongwan Liu, Graduate Student in Physics, MITWritten 154w ago · Upvoted by Jay Wacker, physicist, phd+postdoc+faculty and Don van der Drift, In PhD Physics program for https://www.quora.com/What-is-the-error-function-and-why-is-it-useful-in-physics 2.5 years at Technische Universiteit Eindhoven, former Physics researche…The error function is, essentially, the integral of the standard normal distribution. Specifically, it is related to the actual integral [math]\Phi[/math] by (from Wikipedia)I've come across the error function in my work in two main ways. First, it comes up sometimes when you're dealing with Maxwell-Boltzmann distributions, because the velocities of particles are normally distributed. The integrals of velocity error function distributions in this case give erf functions, and are important in various stability criteria for plasmas in thermal equilibrium. Second, it's sometimes useful as a function to model turn-on curves, for example the behavior of triggers in experiments at the LHC: Triggers are designed to quickly choose events recorded in the detectors at LHC and mark them as interesting. The trigger studied above look for events with a error function table "good-looking" electron with transverse momentum above 15 GeV/c. The plot above shows how often this trigger actually picks events that we think are "good". The points are fitted to the functionwhere A (p_0) is the average efficiency at high transverse momentum and x_0 (p_1) is the "turn-on" (should be 15 GeV ideally).4k Views · View Upvotes · Answer requested by Quora UserRelated QuestionsMore Answers BelowWhat is the physical significance of error function?1,793 ViewsWhat is the physical meaning of error function in quantum mechanics?3,400 ViewsWhy is math so useful in physics?18,128 ViewsWhat is the partition function in physics?12,385 ViewsHow useful is density functional theory to condensed-matter physics?892 Views Erik Yelemanov, Engineering physics studentWritten 154w ago · Upvoted by Ed Caruthers, PhD and post-doc work in Physics at UT Austin. Published papers in electronic properties of metals,…The error function is also present in diffusion. Diffusion is a transport phenomena associated with the random thermal motion of atoms that produces a change in the macroscopic concentration profile. Fick's laws are used to mathematically describe diffusion and are a generalization of the equations of heat transfer used by Fourier.Fick's first law is [math]\mathbf{j_i} = -D_{i} \nabla c_{i}[/math]where [math]j_{i}[/math] is the atomic current, [math]D_{i}[/math] i
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