Proving Stirling's formula.. help

  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. Andrew Mason

    Andrew Mason 6,834
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    Try:
    http://www.sosmath.com/calculus/sequence/stirling/stirling.html

    AM
     
  4. Tide

    Tide 3,143
    Science Advisor
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    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. Thanks for helping.. but I should uuse the substitution t=ny..

    HELP PLZ
     
  6. NateTG

    NateTG 2,537
    Science Advisor
    Homework Helper

  7. Thanks alot..
     
  8. Re: proving Stirling's formula.. help plz

    How can I find equivalent Frenkel defects in the crystal through the equivalent Stralink
     
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