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The th coefficient of this **series can be** computed as (17) where is given by the recurrence equation (18) with initial condition . For |z| < 1, we have erf ( erf − 1 ( z ) ) = z {\displaystyle \operatorname ζ 2 \left(\operatorname ζ 1 ^{-1}(z)\right)=z} . 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 Wolfram Cloud Central infrastructure for Wolfram's cloud products & services. Check This Out

Negative integer values of Im(ƒ) are shown with thick red lines. Documentation Feedback Please complete this field. In order of increasing accuracy, they are: erf ( x ) ≈ 1 − 1 ( 1 + a 1 x + a 2 x 2 + a 3 x Positive integer values of Im(f) are shown with thick blue lines. https://reference.wolfram.com/language/ref/InverseErf.html

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- I also found out that is it okay to put z -> iz in the series above (2) and it fits with result obtained from Maple. –George Nov 7 '14 at
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W. Because when I typed y = Exp[(Erf[I t]^(-1))^2]; Plot[y, {t, -1, 1}] I get this !Mathematica graphics –Nasser Nov 1 '14 at 19:24 1 The $\text{erf}^{-1}(x)$ is not $\frac{1}{\text{erf}(x)}$, but The pairs of functions {erff(),erfcf()} and {erfl(),erfcl()} take and return values of type float and long double respectively. Inverse Erfc Softw., 19 (1): 22–32, doi:10.1145/151271.151273 ^ Zaghloul, M.

Wolfram Knowledgebase Curated computable knowledge powering Wolfram|Alpha. Inverse Error Function Calculator DetailsDetails Mathematical function, suitable for both symbolic and numerical manipulation. It has the derivative (9) and its integral is (10) (which follows from the method of Parker 1955). additional hints How to photograph distant objects (10km)?

M.♦ 68.2k8208336 answered Nov 2 '14 at 17:18 DumpsterDoofus 8,8661636 This looks amazing, thank you for help. Inverse Complementary Error Function H. M. p.297.

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 Support FAQ Wolfram Community Contact Support Premium Support Premier Service Technical Services All Support & Learning » Company About Company Background Wolfram Blog News Events Contact Us Work with Us Careers Erf(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 Inverse Error Function Excel 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

A visual proof of this fact can be obtained by plotting the sign of the imaginary component of $\text{Erf}(z)$ times a function which has peaks when the phase of $\text{Erf}(z)$ is his comment is here Java: Apache commons-math[19] provides implementations of erf and erfc for real arguments. Google search: Google's search also acts as a calculator and will evaluate "erf(...)" and "erfc(...)" for real arguments. Zwillinger, D. Inverse Error Function Matlab

and Watson, G.N. Definite integrals are given by (11) (12) (13) (14) (OEIS A087197 and A114864), where is the Euler-Mascheroni constant and is the natural logarithm of 2. Sciences Astronomy Biology Chemistry More... http://btcherb.com/error-function/inverse-of-the-error-function.php 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

IEEE Transactions on Wireless Communications, 4(2), 840–845, doi=10.1109/TWC.2003.814350. ^ Chang, Seok-Ho; Cosman, Pamela C.; Milstein, Laurence B. (November 2011). "Chernoff-Type Bounds for the Gaussian Error Function". Inverse Error Function Python and Stegun, I.A. (Eds.). "Repeated Integrals of the Error Function." §7.2 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. The inverse error function is usually defined with domain (−1,1), and it is restricted to this domain in many computer algebra systems.

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 & Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the 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 Converse Error N ! ∫ x ∞ t − 2 N e − t 2 d t , {\displaystyle R_ − 7(x):={\frac {(-1)^ − 6}{\sqrt {\pi }}}2^ − 5{\frac {(2N)!} − 4}\int _

DetailsDetails Mathematical function, suitable for both symbolic and numerical manipulation. For certain special arguments, InverseErf automatically evaluates to exact values. This directly results from the fact that the integrand e − t 2 {\displaystyle e^{-t^ − 2}} is an even function. navigate here Computerbasedmath.org» Join the initiative for modernizing math education.

Ch.5 in Combinatorial Species and Tree-Like Structures. Documentation Feedback Please complete this field. Weisstein. "Bürmann's Theorem" from Wolfram MathWorld—A Wolfram Web Resource./ E. Conf., vol. 2, pp. 571–575. ^ Van Zeghbroeck, Bart; Principles of Semiconductor Devices, University of Colorado, 2011. [1] ^ Wolfram MathWorld ^ H.

Erfc automatically threads over lists. In it, you'll get: The week's top questions and answers Important community announcements Questions that need answers see an example newsletter By subscribing, you agree to the privacy policy and terms

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