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# Inverse Error Function Expansion

## Contents

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 / Arts Culture / Recreation At the imaginary axis, it tends to ±i∞. The integrand ƒ=exp(−z2) and ƒ=erf(z) are shown in the complex z-plane in figures 2 and 3. What is the exchange interaction? http://mathworld.wolfram.com/InverseErf.html

## Erf(2)

And why? After division by n!, all the En for odd n look similar (but not identical) to each other. J.; Lozier, Daniel M.; Boisvert, Ronald F.; Clark, Charles W., NIST Handbook of Mathematical Functions, Cambridge University Press, ISBN978-0521192255, MR2723248 External links MathWorld – Erf Authority control NDL: 00562553 Retrieved from The error and complementary error functions occur, for example, in solutions of the heat equation when boundary conditions are given by the Heaviside step 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 Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. SEE ALSO: Confidence Interval, Erf, Inverse Erfc, Probable Error RELATED WOLFRAM SITES: http://functions.wolfram.com/GammaBetaErf/InverseErf/, http://functions.wolfram.com/GammaBetaErf/InverseErf2/ REFERENCES: Bergeron, F.; Labelle, G.; and Leroux, P. Erf Function Calculator M.♦ 68.2k8208336 asked Nov 1 '14 at 19:16 George 536 Can you show the Mathematica code?

W. Springer-Verlag. 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 ) = J.

The Maclaurin series of is given by (15) (OEIS A002067 and A007019). Erf(inf) Browse other questions tagged special-functions or ask your own question. IEEE Transactions on Communications. 59 (11): 2939–2944. The error function and its approximations can be used to estimate results that hold with high probability.

• Cody's algorithm.[20] Maxima provides both erf and erfc for real and complex arguments.
• Comp. 23 (107): 631–637.
• Additional unrelated fun stuff: the $\text{Erf}$ function maps purely imaginary values to purely imaginary values in a 1-to-1 manner, so it makes sense that $\text{Erf}^{-1}(iz)=if(z)$ for some real-valued function $f$.

## Inverse Error Function Calculator

Asymptotic expansion A useful asymptotic expansion of the complementary error function (and therefore also of the error function) for large real x is erfc ⁡ ( x ) = e − http://arxiv.org/abs/math/0607230 Generated Wed, 19 Oct 2016 02:16:14 GMT by s_nt6 (squid/3.5.20) Erf(2) If L is sufficiently far from the mean, i.e. μ − L ≥ σ ln ⁡ k {\displaystyle \mu -L\geq \sigma {\sqrt {\ln {k}}}} , then: Pr [ X ≤ L Inverse Error Function Excel more stack exchange communities company blog Stack Exchange Inbox Reputation and Badges sign up log in tour help Tour Start here for a quick overview of the site Help Center Detailed

Applications When the results of a series of measurements are described by a normal distribution with standard deviation σ {\displaystyle \textstyle \sigma } and expected value 0, then erf ( a check over here How to Cite Customize Annotate UnAnnotate What's New About the Project 7 Error Functions, Dawson’s and Fresnel IntegralsProperties7.16 Generalized Error Functions7.18 Repeated Integrals of the Complementary Error Function §7.17 Inverse Error Functions Referenced by: You can always check the quality of your series approximation $\text{Erf}^{-1}(iz)$ by feeding the result to Erf and see how close the result is to $iz$. It satisfies the equation (8) where is the inverse erfc function. Inverse Erf

Generated Wed, 19 Oct 2016 02:16:14 GMT by s_nt6 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.9/ Connection Math. 13, 459-470, 1963. The error function at +∞ is exactly 1 (see Gaussian integral). his comment is here The inverse complementary error function is defined as erfc − 1 ⁡ ( 1 − z ) = erf − 1 ⁡ ( z ) . {\displaystyle \operatorname ζ 8 ^{-1}(1-z)=\operatorname

LCCN64-60036. Error Function Table The system returned: (22) Invalid argument The remote host or network may be down. share|improve this answer edited Aug 23 '15 at 5:00 J.

## Not the answer you're looking for?

Handbook of Continued Fractions for Special Functions. It has the derivative (9) and its integral is (10) (which follows from the method of Parker 1955). Math. Erf Function Excel The Q-function can be expressed in terms of the error function as Q ( x ) = 1 2 − 1 2 erf ⁡ ( x 2 ) = 1 2

I tried to use some approximations of inverse error functions, such as $$\text{erf}^{-1}(x) = \sum_{k=0}^{N} \frac{c_k}{2k+1}\left(\frac{\sqrt \pi}{2}x\right)^{2k+1}, (2)$$ to finite $N$ (from http://en.wikipedia.org/wiki/Error_function#Inverse_functions) which holds if $x \in [-1,1]$ and MR0167642. This usage is similar to the Q-function, which in fact can be written in terms of the error function. http://shpsoftware.com/error-function/inverse-error-function-c.php Hints help you try the next step on your own.

Generated Wed, 19 Oct 2016 02:16:14 GMT by s_nt6 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.10/ Connection The code I use is Plot[{Re[Exp[InverseErf[I x]]^2], Im[Exp[InverseErf[I x]]^2]}, {x, -1, 1}] –George Nov 1 '14 at 19:54 From help for InverserErf it says Explicit numerical values are given Contact the MathWorld Team © 1999-2016 Wolfram Research, Inc. | Terms of Use THINGS TO TRY: inverse erf .1234 with the last 2 digits repeating Dini's surface Error function From Wikipedia, For complex, the Faddeeva package provides a C++ complex implementation.

Monthly 62, 439-440, 1955. Intermediate levels of Im(ƒ)=constant are shown with thin green lines. Keywords: error functions Permalink: http://dlmf.nist.gov/7.17.iii See also: info for 7.17 As x→0 7.17.3 inverfc⁡x∼u-1/2+a2⁢u3/2+a3⁢u5/2+a4⁢u7/2+⋯, Symbols: ∼: Poincaré asymptotic expansion, inverfc⁡x: inverse complementary error function, x: real variable, ai: coefficients and u: W.

We analyze the derivatives $\frac{d^{n}}{dz^{n}} \operatorname*{inverf}(z) |_{z=0}$, as $n\to \infty$ using nested derivatives and a discrete ray method. Weisstein ^ Bergsma, Wicher. "On a new correlation coefficient, its orthogonal decomposition and associated tests of independence" (PDF). ^ Cuyt, Annie A. All generalised error functions for n>0 look similar on the positive x side of the graph. Flour shortage in baking Are leet passwords easily crackable?

Have you tried that, to see if your approximation is any good? –DumpsterDoofus Nov 2 '14 at 15:47 | show 3 more comments 1 Answer 1 active oldest votes up vote Why does Mal change his mind? Please try the request again. http://mathworld.wolfram.com/InverseErf.html Wolfram Web Resources Mathematica» The #1 tool for creating Demonstrations and anything technical.

While the mark is used herein with the limited permission of Wolfram Research, Stack Exchange and this site disclaim all affiliation therewith. The error function is a special case of the Mittag-Leffler function, and can also be expressed as a confluent hypergeometric function (Kummer's function): erf ⁡ ( x ) = 2 x current community blog chat Mathematica Mathematica Meta your communities Sign up or log in to customize your list.