# Proving Stirling's formula.. help

by Physicist
Tags: formula, proving, stirling
 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
HW Helper
P: 6,674
 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
 Sci Advisor HW Helper P: 3,144 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.
 P: 43 Proving Stirling's formula.. help Thanks for helping.. but I should uuse the substitution t=ny.. HELP PLZ
 Sci Advisor HW Helper P: 2,537
 P: 43 Thanks alot..
 P: 7 How can I find equivalent Frenkel defects in the crystal through the equivalent Stralink

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