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Proving Stirling's formula.. help

by Physicist
Tags: formula, proving, stirling
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Physicist
#1
Nov26-04, 04:06 PM
P: 43
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..

Can anyone help?

(How can I write the mathematical symbols here?)

Thanks
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Andrew Mason
#2
Nov26-04, 04:18 PM
Sci Advisor
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Quote Quote by 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..

Can anyone help?

(How can I write the mathematical symbols here?)

Thanks
Try:
http://www.sosmath.com/calculus/sequ.../stirling.html

AM
Tide
#3
Nov26-04, 04:35 PM
Sci Advisor
HW Helper
P: 3,147
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.

Physicist
#4
Nov27-04, 10:13 PM
P: 43
Proving Stirling's formula.. help

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

HELP PLZ
NateTG
#5
Dec3-04, 11:39 AM
Sci Advisor
HW Helper
P: 2,538
http://mathworld.wolfram.com/Stirlin...oximation.html
Physicist
#6
Dec3-04, 04:30 PM
P: 43
Thanks alot..
nafaa
#7
Jan5-12, 04:12 PM
P: 7
How can I find equivalent Frenkel defects in the crystal through the equivalent Stralink


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