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Expressing as a single sum.

  1. Oct 17, 2005 #1
    I know this is pretty easy, but for this particular question I'm having difficulty.
    its for the Power series solution of the DE y''+yx=0

    \sum\limits_{n = 0}^\infty {(n - 1)nC_n } x^{n - 2} + \sum\limits_0^\infty {C_n } x^{n + 1} [/tex]

    This is ths sum I've come up with and I need to express it as a single sum. I can't seem to do it though. Any help will be greatly appreciated.
  2. jcsd
  3. Oct 17, 2005 #2
    Well, what do you know about the sum of series with the same indices?
  4. Oct 17, 2005 #3
    The index of your first sum is not correct.

    Remember that every time you take a derivative you loose a constant term.

    After you correct your index you can then change it to something more desirable.
  5. Oct 17, 2005 #4


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    Incidentally, if you didn't know, your DE is just a variant Airy's Equation (with x replaced by -x) and represents waves propagating in a medium whose properties (index of refraction, water depth, etc.) vary linearly in space.
  6. Oct 17, 2005 #5
    Excellent. Thanks for the help.

    I believe we study Airy's equations in greater detail later on in the course. We touched on them briefly in my Quantum Physics class last semester though. :D
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