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Estimating Error Functions for very large values

  1. Sep 14, 2011 #1
    Hey guys,
    I was posed an interesting problem which relates to upsizing quantum physics, that boils down to a math problem. I was trying to calculate the probability that a 1000 tonne bridge would be found 1m from its resting position, if you model it as having the ground energy of a harmonic oscillator.
    Eventually the problem boils down to calculating 1 - Erf(7.79x10[itex]^{19}[/itex])
    which is the same as calculating Erfc of 7.79x10[itex]^{19}[/itex]
    as you might be able to figure out the number is unbelievably small.
    i was womdering if anyone might have a good approximation to it, or an interesting way to calculate it on mathematica/matlab?
    ive given a few approximations a try already, but have been rather disappointed with the results.
     
  2. jcsd
  3. Sep 14, 2011 #2

    lurflurf

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    You are dealing with a very small number.
    An asymptotic_expansion is a good choice here, read about it in any nice calculus book. We can think of it as almost the Taylor expansion of f(1/x) about x=0 of of f(x) about x=infinity.
    for large x
    1-erf(x)~(e^-x^2/sqr(pi)) [1/x-1/(2x^3)+3/(4x^5)-15/(8x^7)+105/(16x^9)+...]
    The general term being (-1)^n (2n-1)!!/[x(2x^2)^n] for n=0,1,2,...

    http://en.wikipedia.org/wiki/Error_function
     
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