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!

Gamma function

  1. Aug 4, 2015 #1
    This is given in Mathematical methods for physicists by Arfken and weber, while defining a property of gamma function, I have no idea how the term in the red circle becomes 'z' in the final step, please help

    Attached Files:

  2. jcsd
  3. Aug 4, 2015 #2
    Try multiplying the numerator and denominator by z and pull out an n from the exponent then rearrange terms.
  4. Aug 4, 2015 #3
    I'm asking about the final step, How to get the final step from the second step?
  5. Aug 4, 2015 #4
    The limit of the product is product of the limit of the factors. What is the definition of the gamma function?
  6. Aug 4, 2015 #5
    I know the limit of the second term in the product converges to "gamma of z', it is how the gamma function is defined, But I couldn't figure out how the limit of the first term in the product converges to 'z'. How do I compute it?
  7. Aug 4, 2015 #6


    User Avatar
    Science Advisor

    So you are asking specifically about
    [tex]\lim_{n\to \infty} \frac{nz}{z+ n+ 1}[/tex]

    Divide both numerator and denominator by n:
    [tex]\lim_{n\to\infty}\frac{z}{\frac{z}{n}+ 1+ \frac{1}{n}}[/tex]
  8. Aug 4, 2015 #7
    nz/(n+z+1) → nz/n in the limit n→∞
  9. Aug 5, 2015 #8
    Yeah that's what I asked for, Thank you!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook