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Topic: e^(-x^2) and Erf[x]
Replies: 10   Last Post: Feb 3, 2000 12:19 PM

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Doug Kuhlmann

Posts: 3,630
Registered: 12/6/04
Re: e^(-x^2) and Erf[x]
Posted: Feb 1, 2000 9:49 PM
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Notes from several folks in this message:

>>Erf[x] = (2/ Sqrt[Pi]) Integrate[ e^(-t^2),{t,0,x} ].

(Aside: I've seen erf(x) defined as above without the 2/sqrt[Pi})

>>I think the real problem is not with the lack of "erf" but with the
>>idea that "not integrable in terms of elementary functions" means
>>"not integrable". Any reasonable function is integrable; and we're always
>>welcome to name that integral with some new function if we feel like
>>the shorthand is worthwhile.


>Exactly. Beyond that, e^(-x^2) *is* more than just "any reasonable
>so making it "more equal than others" in this regard and giving its integral a
>standard name that students are expected to recognize is entirely
>Seriously arguing that it and its integral (with the appropriate fudge factor)
>then fall into the same category of importance as 1/x and the log function is
>quite another matter.

We can easily compute erf(x) (modulo the constant in front) on the TI-83 by
using Normcdf.

Normcdf(a,b) = (1/Sqrt(2Pi))*Int(e^(-t^2)), t, a, b)

So erf already can have the cachet of being easily computable on a caclculator.


Doug Kuhlmann
Math Department
Phillips Academy
180 Main Street
Andover, MA 01810

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