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




Re: e^(x^2) and Erf[x]
Posted:
Feb 1, 2000 9:49 PM


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 >function" >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 >appropriate. >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 TI83 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
Doug Kuhlmann Math Department Phillips Academy 180 Main Street Andover, MA 01810 dkuhlmann@andover.edu



