Error Function Proof
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Error Function Matlab
unclear what you're asking by Micah, Adriano, Dominic Michaelis, Danny Cheuk, draks ... Jul 24 '13 at 5:30 Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question.If this question can be reworded to fit the rules in the help center, please edit the question. 4 isn't the error function defined over the integral ? –Dominic Michaelis Apr 17 '13 at 5:12 2 By definition, $$\text{erf}(x)=\frac2{\sqrt\pi}\int_0^x\exp(-w^2)\,dw.$$ Is this a different definition than you've been given? Also, since your integral is indefinite, don't forget your constant of integration. –Cameron Buie Apr 17 '13 at 5:17 add a comment| 1 Answer 1 active oldest votes up vote 3 down vote accepted There's nothing here to prove, the definition of the error function is that $$ \text{erf}(x)=\frac{2}{\sqrt{\pi}}\int_0^x e^{-x^2}dx $$ I suppose that you might be interested in why the $\frac{2}{\sqrt{\pi}}$. Basically, it works like this: let $$ I = \int_0^\infty e^{-x^2}dx $$ Now, we can state that $$\begin{align} I^2 &= \int_0^\infty e^{-x^2}dx\int_0^\infty e^{-y^2}dy\\ &=\int_0^\infty\int_0^\infty e^{-(x^2+y^2
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Error Function Excel
Events Pets Politics & Government Pregnancy & Parenting Science & Mathematics Social Science complementary error function table Society & Culture Sports Travel Yahoo Products International Argentina Australia Brazil Canada France Germany India Indonesia Italy Malaysia Mexico New error function python Zealand Philippines Quebec Singapore Taiwan Hong Kong Spain Thailand UK & Ireland Vietnam Espanol About About Answers Community Guidelines Leaderboard Knowledge Partners Points & Levels Blog Safety Tips Science & Mathematics Mathematics Next http://math.stackexchange.com/questions/364112/how-to-prove-that-integration-of-exp-x2-is-error-function How to prove that the Error Function is an odd function? I am in a statistics course and I am wondering how I can prove that the Error function, or: erf(x) = (2/sqrt(pi))(integral e^-t^2 from 0 to x) is an odd function. I think I should use change of variables, but i'm not sure. Thanks! Follow 1 answer 1 Report Abuse Are you sure you https://answers.yahoo.com/question/index?qid=20140117120635AACyVqq want to delete this answer? Yes No Sorry, something has gone wrong. Trending Now Ohio State football Michael Jackson Daniela Ryf Haley Bennett Fantasy Football Bathroom Vanities Sasha Banks Linda McCartney Luxury SUV Deals Joey Bosa Answers Best Answer: Yes, a simple change of variables in the integral will do it: erf(-x) = (2/sqrt(pi))(integral e^-t^2 dt from 0 to -x) substitute u = -t, du = -dt: erf(-x) = (2/sqrt(pi)(integral -e^-(-u)^2 du from 0 to x) (-u)^2 = u^2, and you can bring the negative out front: erf(-x) = - (2/sqrt(pi))(integral e^-u^2 du from 0 to x) erf(-x) = - erf(x) So erf is an odd function. Source(s): PD3 · 3 years ago 0 Thumbs up 0 Thumbs down Comment Add a comment Submit · just now Asker's rating Report Abuse Add your answer How to prove that the Error Function is an odd function? I am in a statistics course and I am wondering how I can prove that the Error function, or: erf(x) = (2/sqrt(pi))(integral e^-t^2 from 0 to x) is an odd function. I think I should use change of variables, but i'm not sure. Thanks! Add your answer Source Submit Ca
Community Forums > Science Education > Homework and Coursework Questions > Calculus and Beyond Homework > Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors https://www.physicsforums.com/threads/error-function.371829/ Dismiss Notice Dismiss Notice Join Physics Forums Today! The friendliest, high quality science https://www.youtube.com/watch?v=PBSFXukqztU and math community on the planet! Everyone who loves science is here! Error Function Jan 22, 2010 #1 Bachelier How do we prove that the error function erf(x) and the Fresnal integral are odd functions? Bachelier, Jan 22, 2010 Phys.org - latest science and technology news stories on Phys.org •Game over? Computer beats error function human champ in ancient Chinese game •Simplifying solar cells with a new mix of materials •Imaged 'jets' reveal cerium's post-shock inner strength Jan 22, 2010 #2 Dick Science Advisor Homework Helper Bachelier said: ↑ How do we prove that the error function erf(x) and the Fresnal integral are odd functions? By using the definition of each one. They are all integrals of some even function from 0 error function table to x. Isn't that always odd? Dick, Jan 22, 2010 Jan 22, 2010 #3 Bachelier OK, let me ask the question is a different way: [tex]{erf}(x)=\frac{2}{\sqrt{\pi}}\int_0^x e^{-t^2} dt[/tex] How do I prove that? [tex]{erf}(-x) = - {erf}(x)[/tex] Last edited: Jan 22, 2010 Bachelier, Jan 22, 2010 Jan 22, 2010 #4 Dick Science Advisor Homework Helper Ok, let me pose the solution in a different way. f(t) is even, like e^(-t^2), i.e. f(-t)=f(t). Let F(x)=integral f(t)*dt from 0 to x. Do a change of variable from t to u=(-t). What happens? Don't you get F(x)=(-F(-x))? Isn't that odd? Dick, Jan 22, 2010 Jan 22, 2010 #5 Bachelier Thanks Dick. After deep thought, I think I got it now. I was missing one piece of information. I didn't know that the integral of an even function on 0 to infinity is an odd function. I am going to explain my understanding below and please correct me if I am wrong, thanks in advance. :) [tex]\int_0^x f(t) dt = F(x) - F(0)[/tex] Based on the fundamental theorem of calculus. F(0) = 0 so we have now: [tex]\int_0^x f(t) dt = F(x)[/tex] [tex]\int_0^x f(t) dt = -(-F(x))[/tex] [tex]\int_0^x f(t) dt =-(F(-x))[/tex]
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