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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
     

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  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

    HallsofIvy

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    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!
     
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