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Here's a Wiki article on the subject. Sadly it doesn't do a good job of explaining the significance of the function.

Of course it may mean different things to different people (for mathematicians it may be important for reasons entirely different from the reasons it is important to engineers). The following is a hypothetical problem explaining the significance I am looking for.

A laser printer has a targeting system where a laser is supposed to mark a paper at say x=6cm. The standard deviation measured on a large number of attempts to mark the ordinate turns out to be 0.1 cm. If say a billion attempts are made to target x=6cm, what is the maximum expected ordinate that will be marked? Does the error function help me in solving such problems?

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It is closely---trivially---related to the cumulative distribution function of the standard normal distribution. – Michael Hardy Aug 29 '12 at 21:23
Error function usually does not help you to do something. It is not an equation you get and use it. It comes out from the derivations of your own problem. Almost all such problems have exponentials. – Seyhmus Güngören Aug 29 '12 at 21:51
You do not explain why the Wiki article on the subject would not do a good job of explaining the significance of the function. Care to expand? – Did Oct 14 '12 at 10:38
I would like to contrast that with the wiki article on normal distribution ( It does a really good job of explaining how normal function is relevant and how it affects numerous physical phenomena. Here I am referring to the the subsections "Occurrence" and "History", which in my opinion do justice to the subject. The error function just has a small subsection ( The article is good but provides little insight. I am not an expert, but I assume that both articles are technically sound. – Shashank Sawant Oct 14 '12 at 19:39
In other words, you seek some more Applications of the error function. If so, you might wish to rephrase your question. (And please use @ to signal your comments.) – Did Oct 14 '12 at 22:48

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