Calculating erf(x)?

  1. Hi guys...
    don't suppose anybody knows how to calculate the error function - erf(x)

    I know Matlab can calculate it - but is it possible to evaluate it without computational techniques (i.e. using computers)?

    [tex] {erf}(x) = \frac{2}{\sqrt{\pi}}\int_0^x e^{-t^2} dt.[/tex]

    Would appreciate any feedback.

    thanks.

    The link below will direct you to a website where the equation can be viewed...

    http://images.planetmath.org:8080/cache/objects/6429/l2h/img2.png
     
    Last edited by a moderator: Aug 10, 2006
  2. jcsd
  3. HallsofIvy

    HallsofIvy 40,549
    Staff Emeritus
    Science Advisor

    If you mean "Is there an elementary anti-derivative" that can be evaluated directly, the answer is no. The only way to evaluate erf(x) is to do a numerical integration.
     
  4. thanks...
    by numerical integration do you mean applying Tayler Series and expansions like that?
     
  5. HallsofIvy

    HallsofIvy 40,549
    Staff Emeritus
    Science Advisor

    I was thinking more of Simpson's rule.
     
  6. actually, with a computer program to calculate the terms and summation, that is what they do. one thing is that there is a nice closed form expression for the erf(x) for large x.

    see http://mathworld.wolfram.com/Erf.html for some detail.
     
  7. thanks guys!
     
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