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Weird Generating Function prove

  1. May 28, 2004 #1
    Q: show that (1-4x)^(-1/2) generates the sequence 2n chooses n, n is defined as natural

    All the formulas I have requires integer exponent. I am not sure how to deal with (-1/2).

    Thanks for any input!!!
  2. jcsd
  3. May 28, 2004 #2

    Dr Transport

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    Science Advisor
    Gold Member

    expand the function in a Taylor series

    [tex] f(x) = f(0) + x\frac{df(x)}{dx}|_0 +\frac{x}{2!}\frac{d^{2}f(x)}{dx^{2}}|_0 + ... [/tex]

    differentiate your function

    [tex] \frac{1}{\sqrt{1-4x}}[/tex]

    as you normally would, for example the first derivative is [tex] \frac{2x}{(1-4x)^{3/2}} [/tex].
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