Inverse Error Function Mathematica
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Inverse Erfc
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Series representations (8 formulas) http://functions.wolfram.com/GammaBetaErf/InverseErf/ Differential equations (1 formula) Differentiation (5 formulas) Integration (1 formula) Representations through more general functions (1 formula) Representations through equivalent functions (2 formulas) Zeros (1 formula) History (0 formulas) InverseErf[z1,z2]
Mathematica Wolfram|Alpha Appliance Enterprise Solutions Corporate Consulting Technical Services Wolfram|Alpha Business Solutions Products for Education Wolfram|Alpha Wolfram|Alpha Pro Problem Generator API Data Drop Mobile https://reference.wolfram.com/language/ref/InverseErfc.html Apps Wolfram Cloud App Wolfram|Alpha for Mobile Wolfram|Alpha-Powered Apps Services Paid Project Support Training Summer Programs All Products & Services » Technologies Wolfram Language Revolutionary knowledge-based http://mathematica.stackexchange.com/questions/64635/inverse-error-function programming language. Wolfram Cloud Central infrastructure for Wolfram's cloud products & services. Wolfram Science Technology-enabling science of the computational universe. Computable Document Format Computation-powered interactive error function documents. Wolfram Engine Software engine implementing the Wolfram Language. Wolfram Natural Language Understanding System Knowledge-based broadly deployed natural language. Wolfram Data Framework Semantic framework for real-world data. Wolfram Universal Deployment System Instant deployment across cloud, desktop, mobile, and more. Wolfram Knowledgebase Curated computable knowledge powering Wolfram|Alpha. All Technologies » Solutions inverse error function Engineering, R&D Aerospace & Defense Chemical Engineering Control Systems Electrical Engineering Image Processing Industrial Engineering Mechanical Engineering Operations Research More... 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 Statistics More... Sciences Astronomy Biology Chemistry More... Trends Internet of Things High-Performance Computing Hackathons All Solutions » Support & Learning Learning Wolfram Language Documentation Fast Introduction for Programmers Training Videos & Screencasts Wolfram Language Introductory Book Virtual Workshops Summer Programs Books Need Help? 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 at Wolfram Internships Other Wolfram Language Jobs Initiatives Wolfram Foundation MathWorld Computer-Based Math A New Kind of Science Wolfram Technology for Hackathons Student Ambassa
here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company Business Learn more about hiring developers or posting ads with us Mathematica Questions Tags Users Badges Unanswered Ask Question _ Mathematica Stack Exchange is a question and answer site for users of Mathematica. 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 top Inverse error function up vote 6 down vote favorite I solved some equation in Mathematica and I obtained something like $$y(t)=\exp \left\lbrace \left[ \text{erf}^{-1} (\text{i}t) \right]^2\right\rbrace, (1)$$ where $\text{i}$ is imaginary unit and $\text{erf}^{-1}(x)$ is the inverse error function (it is not equal to $\frac{1}{\text{erf}(x)}$ !!), which is defined for $x \in [-1,1]$. The problem is that the $t$ is real and the function has to be also real, but I can't plot this function since $\text{erf}^{-1}$ accepts only real arguments in Mathematica. Is there any way how to plot the solution or convert it to some other expression, which can be plotted? 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 then I just simply put $t \rightarrow \text{i}t$ in approximated version of (1) and obtained only real part (imaginary part was zero), but I'm not sure wheather it is correct. special-functions share|improve this question edited Aug 23 '15 at 4:58 J. M.♦ 68.2k8208336 asked Nov 1 '14 at 19:16 George 536 Can you show the Mathematica code? 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 an inverse function of $\text{erf}(x)$, as explained above. The $\text{erf}^{-1}(x)$ function is represented in Mathematica as InverseErf[x]. 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 only for real values of s between -1 and +1. But