1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Homework Helper
    Gold Member

    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 :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook