proving Stirling's formula.. help plz

[Physicist]

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

[Andrew Mason]

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

AM

[Tide]

Another approach would be to use the method of steepest descent. Basically, you can find where t^n e^{-t} is a maximum and observe that the most significant contribution to the integral comes from near that maximum.

[Physicist]

Thanks for helping.. but I should uuse the substitution t=ny..

HELP PLZ

[NateTG]

http://mathworld.wolfram.com/StirlingsApproximation.html

[Physicist]

Thanks alot..