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Gamma function (infinite product representation)

  • Thread starter math8
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  • #1
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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.
 

Answers and Replies

  • #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:
  • #3
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Thanks a lot :)
 

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