1. Not finding help here? Sign up for a free 30min 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!

Evaluating the n-th difference

  1. Jul 17, 2007 #1
    hi, my problem is to evaluate the n-th difference to be able to approximate the n-th derivative of a function f(x) at the point x=0

    as for small 'h' then [tex] \frac{\Delta ^{n}}{h^{n} \sim \frac{d^{n}f(0)}{dx^{n}} [/tex]

    i think that the n-th difference (with step h) has the representation:

    [tex] \Delta ^{n} f(0) = \frac{1}{2\pi i} \int_{c-i\infty}^{c+i\infty}ds \frac{f(s)}{(s(s-h)(s-2h)(s-3h).....(s-nh)}x^{s} [/tex]

    and that evaluating this we could obtain an (approximate) asymptotic expansion for n-->infinity.

    the intention is given a generating function

    [tex] f(x)= a(0)+a(1)x+a(2)x^{2}+..................... [/tex]

    then to calculate a(n) you need to know the n-th derivative, we can approximate this derivative by the n-th forward difference at x=0 with an small step 'h'
     
  2. jcsd
  3. Jul 18, 2007 #2

    lurflurf

    User Avatar
    Homework Helper

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?