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Gamma function

  1. Feb 6, 2012 #1
    1. The problem statement, all variables and given/known data

    Express [itex]\Gamma (n+\frac{1}{2})[/itex] for [itex]n\in\mathbb{Z}[/itex] in terms of factorials (separately for positive and negative [itex]n[/itex]).

    2. Relevant equations



    3. The attempt at a solution

    I've got for [itex]n\geqslant 0[/itex] that [tex]\displaystyle \Gamma \left(n+\frac{1}{2} \right) = \frac{(2n-1)!!}{2^n} \sqrt{\pi}[/tex] but what do I do when [itex]n<0[/itex] ?
     
  2. jcsd
  3. Feb 6, 2012 #2

    vela

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    The same thing. Use ##n\Gamma(n)=\Gamma(n+1)##, so ##(-1/2)\Gamma(-1/2) = \Gamma(1/2)## and so on.
     
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