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Gamma function (infinite product representation)

  1. Mar 18, 2010 #1
    I have come across this expression in some notes

    [tex]\Gamma[/tex] (z) = [tex]\frac{1}{z}[/tex] [tex]\prod[/tex] [tex]\frac{(1+ \frac{1}{n})^{z}}{1+ \frac{z}{n}}[/tex]

    Do you think it's accurate? I have some doubts because I have looked for it on wokipedia, and I couldn't find it.
     
  2. jcsd
  3. Mar 18, 2010 #2

    gabbagabbahey

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    Do you mean

    [tex]\Gamma(z)=\frac{1}{z}\prod_{n=1}^{\infty} \frac{\left(1+\frac{1}{n}\right)^z}{1+\frac{z}{n}}[/tex]

    If so, then yes, it's correct for all complex numbers [itex]z[/itex] except for zero and negative integers.
     
    Last edited: Mar 18, 2010
  4. Mar 18, 2010 #3
    Thanks a lot :)
     
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