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In particular, we **have $$\text{Erf}^{-1}(iz)=i\text{Erfi}^{-1}(z)$$ which means $$y(t)=\exp\left(-\text{Erfi}^{-1}(t)^2\right)$$ and** $\text{Erfi}$ is purely real-valued for real $t$. For previous versions or for complex arguments, SciPy includes implementations of erf, erfc, erfi, and related functions for complex arguments in scipy.special.[21] A complex-argument erf is also in the arbitrary-precision arithmetic Numerical approximations[edit] Over the complete range of values, there is an approximation with a maximal error of 1.2 × 10 − 7 {\displaystyle 1.2\times 10^{-7}} , as follows:[15] erf ( Why was the identity of the Half-Blood Prince important to the story? http://btcherb.com/error-function/inverse-error-function-asymptotic-expansion.php

Written in simplified form so that the coefficient of is 1, (16) (OEIS A092676 and A092677). J. Positive integer values of Im(f) are shown with thick blue lines. The Q-function can be expressed in terms of the error function as Q ( x ) = 1 2 − 1 2 erf ( x 2 ) = 1 2

For large enough values of x, only the first few terms of this asymptotic expansion are needed to obtain a good approximation of erfc(x) (while for not too large values of Are non-english speakers better protected from (international) Phishing? Another approximation is given by erf ( x ) ≈ sgn ( x ) 1 − exp ( − x 2 4 π + a x 2 1 Comments: 25 pages, 6 figures Subjects: Classical Analysis and ODEs (math.CA) MSCclasses: 33B20 (Primary); 30B10, 34K25 (Secondary) Citeas: arXiv:math/0607230 [math.CA] (or arXiv:math/0607230v2 [math.CA] for this version) Submission history From: Diego

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- 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
- 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

Online Integral **Calculator» Solve integrals with** Wolfram|Alpha. ISBN 978-0-486-61272-0. The th coefficient of this series can be computed as (17) where is given by the recurrence equation (18) with initial condition . Erf Function Calculator 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 −

Google search: Google's search also acts as a calculator and will evaluate "erf(...)" and "erfc(...)" for real arguments. Inverse Error Function Calculator Julia: Includes erf and erfc for real and complex arguments. 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 http://dlmf.nist.gov/7.17 Go: Provides math.Erf() and math.Erfc() for float64 arguments.

special-functions share|improve this question edited Aug 23 '15 at 4:58 J. Erf(inf) The advantage of this approach is it avoid the use of complicated series approximations, and is still very accurate. Symbols: inverfx: inverse error function and x: real variable Permalink: http://dlmf.nist.gov/7.17.E2 Encodings: TeX, pMML, png See also: info for 7.17(ii) For 25S values of the first 200 coefficients see Strecok (1968). IDL: provides both erf and erfc for real and complex arguments.

Hints help you try the next step on your own. 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 Erf(2) Carlitz, L. "The Inverse of the Error Function." Pacific J. Inverse Error Function Excel 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.

Cody's algorithm.[20] Maxima provides both erf and erfc for real and complex arguments. this contact form 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 ( Craig, A new, simple and exact result for calculating the probability of error for two-dimensional signal constellaions, Proc. 1991 IEEE Military Commun. 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 Inverse Erf

Mathematica Stack Exchange works best with JavaScript enabled Welcome,Guest User registration Login Service How to use Sample calculation Smartphone Japanese Life Calendar Financial Health Enviroment Conversion Utility Education Mathematics Science Professional 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 $f$. Browse other questions tagged special-functions or ask your own question. http://btcherb.com/error-function/inverse-of-error-function.php For complex

Flour shortage in baking Are leet passwords easily crackable? Error Function Table Derivative and integral[edit] The derivative of the error function follows immediately from its definition: d d z erf ( z ) = 2 π e − z 2 . {\displaystyle 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 $iz$.

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 Math. Step-by-step Solutions» Walk through homework problems step-by-step from beginning to end. Erf Function Excel I'm asking how to modify the expression $\text{erf}^{-1}(\text{i}t)$ so it can be plotted. –George Nov 1 '14 at 21:13 It looks like Matlab might be able to do complex

Your cache administrator is webmaster. share|improve this answer edited Aug 23 '15 at 5:00 J. The $\text{erf}^{-1}(x)$ function is represented in Mathematica as InverseErf[x]. http://btcherb.com/error-function/inverse-of-the-error-function.php MR0167642.

The system returned: (22) Invalid argument The remote host or network may be down. The integrand ƒ=exp(−z2) and ƒ=erf(z) are shown in the complex z-plane in figures 2 and 3. Springer-Verlag. M.♦ 68.2k8208336 answered Nov 2 '14 at 17:18 DumpsterDoofus 8,8661636 This looks amazing, thank you for help.

asked 1 year ago viewed 390 times active 1 year ago Blog Stack Overflow Podcast #91 - Can You Stump Nick Craver? 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. The imaginary error function has a very similar Maclaurin series, which is: erfi ( z ) = 2 π ∑ n = 0 ∞ z 2 n + 1 n J. (March 1993), "Algorithm 715: SPECFUN—A portable FORTRAN package of special function routines and test drivers" (PDF), ACM Trans.

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. While the mark is used herein with the limited permission of Wolfram Research, Stack Exchange and this site disclaim all affiliation therewith. But you have complex arguments. –Nasser Nov 1 '14 at 20:10 1 On functions.wolfram.com/GammaBetaErf/InverseErf/04/01 you can read that InverseErf is a function $\mathbb{C} \rightarrow \mathbb{C}$. Is it ok to turn down a promotion?

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. C++: C++11 provides erf() and erfc() in the header cmath. 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 See [2]. ^ http://hackage.haskell.org/package/erf ^ Commons Math: The Apache Commons Mathematics Library ^ a b c Cody, William J. (1969). "Rational Chebyshev Approximations for the Error Function" (PDF).

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

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