The Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.


Math Forum » Discussions » Courses » ap-calculus

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Doug Kuhlmann

Posts: 3,630
Registered: 12/6/04
Re: e^(-x^2) and Erf[x]
Posted: Feb 1, 2000 9:49 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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 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

Doug Kuhlmann
Math Department
Phillips Academy
180 Main Street
Andover, MA 01810
dkuhlmann@andover.edu





Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.