The Integral of e^(x^2)dx
Date: 03/26/98 at 10:37:06 From: Manuel Ruiz Martinez Subject: How should I solve the integral e^(x^2)? First, thank you for answering my letter about Fermat's Last Theorem. I understood some of the concepts that you wrote about there. I am thinking about studying Maths or Physics in the Universidad Complutense in Madrid, or in Valencia. And the question, the integral of e^(x^2). I have a program named Derive. With this program the solution is very strange. I don't know if you will be able to help me, but I think so. Manuel
Date: 03/27/98 at 08:03:54 From: Doctor Jerry Subject: Re: How should I solve the integral e^(x^2)? Hi Manuel, There are many functions - called special functions - which fail to have an anti-derivative expressible as a finite combination of elementary functions. The so-called elliptic functions, the error function, and the gamma function are a few examples. The error function, which is extremely useful in both physics and statistics, is defined as: erf(x) = (2/sqrt(pi))integral from 0 to x of e^(-t^2)dt This is closely related to the problem you mentioned. Neither can be done in finite terms. There would not exist extensive tables of the error function if the anti-derivative of e^(-t^2) were expressible as a finite combination of elementary functions. The Annals can be found in the library of any good university. -Doctor Jerry, The Math Forum http://mathforum.org/dr.math/
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