1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Homework Helper

    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,...

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook