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Thread: Proof using deravatives.

  1. #1
    Junior Member
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    Proof using deravatives.

    Hi,
    Wasn't too sure where to post this so feel free to move.
    If
    $\displaystyle
    \int x^MK(x)dx\not=0
    $
    and
    $\displaystyle \int x^mK(x)dx=0$
    where m = 1,2,3......M-1
    Show that the formula
    $\displaystyle K_{[M+2]}(x)=\frac{3}{2}K_{[M]}(x)+\frac{1}{2}xK'_{[M]}(x)$.
    Produces K of order M+2
    and now
    $\displaystyle
    \int x^{M+2}K(x)dx\not=0
    $

    Any help appreciated cos I don't have a clue where to begin.
    Last edited by markrvr; Jul 30th 2009 at 04:37 AM. Reason: dodgy notation
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  2. #2
    MHF Contributor

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    Quote Originally Posted by markrvr View Post
    Hi,
    Wasn't too sure where to post this so feel free to move.
    If
    $\displaystyle
    k_M=\int t^MKtdt\not=0
    $
    and
    $\displaystyle \int t^mK(t)dt=0$
    where m = 1,2,3......M-1
    Show that the formula
    $\displaystyle K_{[M+2]}(x)=\frac{3}{2}K_{[M]}(x)+\frac{1}{2}xK'_{[M]}(x)$.
    Produces K of order M+2
    Any help appreciated cos I don't have a clue where to begin.
    Your notation is a bit confusing. Is the "$\displaystyle K_{[M]}$" the same as the "$\displaystyle k_M$" in your first equation?
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  3. #3
    Junior Member
    Joined
    Mar 2009
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    Sorry, no they are different. That notation was from a different part I forgot to delete it.
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