Proving Stirling's formula help

  1. Nov 26, 2004 #1
    proving Stirling's formula.. help plz

    How can I prove Stirling's formula?

    n!= integral from 0 to inf. exp(-t) t^n dt= n^n exp(-n) (2 pi n)^0.5

    there's a hint to use the substitution t=ny & ln(1+y) = y- 0.5 y^2

    I tried to use it but I couldn't intgrate.. I tried integrating by parts but it became more complicated.. :frown:

    Can anyone help?

    (How can I write the mathematical symbols here?)

    Thanks
     
    Last edited: Nov 26, 2004
  2. jcsd
  3. Nov 26, 2004 #2

    Andrew Mason

    User Avatar
    Science Advisor
    Homework Helper

    Try:
    http://www.sosmath.com/calculus/sequence/stirling/stirling.html

    AM
     
  4. Nov 26, 2004 #3

    Tide

    User Avatar
    Science Advisor
    Homework Helper

    Another approach would be to use the method of steepest descent. Basically, you can find where [itex]t^n e^{-t}[/itex] is a maximum and observe that the most significant contribution to the integral comes from near that maximum.
     
  5. Nov 27, 2004 #4
    Thanks for helping.. but I should uuse the substitution t=ny..

    HELP PLZ
     
  6. Dec 3, 2004 #5

    NateTG

    User Avatar
    Science Advisor
    Homework Helper

  7. Dec 3, 2004 #6
    Thanks alot..
     
  8. Jan 5, 2012 #7
    Re: proving Stirling's formula.. help plz

    How can I find equivalent Frenkel defects in the crystal through the equivalent Stralink
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Similar Discussions: Proving Stirling's formula help
  1. Prove of formula (Replies: 4)

  2. Help with formula (Replies: 1)

Loading...