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Prove gamma (n+1/2) = (2n!pi^1/2)/(n!4^n) by induction

  1. Mar 14, 2015 #1
    I tried solving this question this way:
    Gamma(n+1/2)
    =(n+1/2-1)gamma(n+1/2-1)
    =(n-1/2)gamma(n-1/2)
    =(2n-1)/2 gamma (2 n-1)/2
    Don't know what to do next
     
  2. jcsd
  3. Mar 14, 2015 #2

    Svein

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    To begin with [itex]\Gamma (\frac{1}{2})=\sqrt{\pi} [/itex]. From there: [itex] \Gamma (1+\frac{1}{2})= \frac{1}{2}\Gamma(\frac{1}{2})=\frac{1}{2}\sqrt{\pi}[/itex]. Checks against the formula.
    Assume that the formula is correct for n. Then [itex]\Gamma(n+1+\frac{1}{2})=(n+\frac{1}{2})\Gamma(n+\frac{1}{2}) [/itex]...
     
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