
#1
Nov2604, 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 



#2
Nov2604, 04:18 PM

Sci Advisor
HW Helper
P: 6,574




#3
Nov2604, 04:35 PM

Sci Advisor
HW Helper
P: 3,149

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.




#4
Nov2704, 10:13 PM

P: 43

proving Stirling's formula.. help plz
Thanks for helping.. but I should uuse the substitution t=ny..
HELP PLZ 



#5
Dec304, 11:39 AM

Sci Advisor
HW Helper
P: 2,538




#6
Dec304, 04:30 PM

P: 43

Thanks alot..




#7
Jan512, 04:12 PM

P: 7

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



Register to reply 
Related Discussions  
proving a formula  Calculus & Beyond Homework  4  
Proving a propositional logic formula  Calculus & Beyond Homework  19  
proving Stirling's formula.. help plz  General Math  0  
Proving Distance Traveled With Formula  Introductory Physics Homework  6  
Proving Gregory's formula  Linear & Abstract Algebra  8 