Prove the following statement
Γ[W(1)] = (Ω - 1)!
^_^
...quite easy...
^_^
2006-10-22 22:45:59 · 8 answers · asked by kevin! 5 in Science & Mathematics ➔ Mathematics
Its easy!!!
Γ[W(1)] is equal to (Ω - 1)!
because of lambert's W function and the gamma function!!
Here's the formula!
W(1)= Ω(the Omega constant)
Its a special Value!!
FOr the gamma function here's the formula!!
Γ(n+1)=n!
therefore
Γ[W(1)] = Γ(Ω)
use the gamma formula!
= (Ω - 1)!
QED!!
Hope that this helps!! ^_^!!
2006-10-25 00:02:37 · answer #1 · answered by Anonymous · 0⤊ 0⤋
The gamma function extends the factorial function from integers to reals (and complex):
Γ( n ) = (n-1)!
Perhaps "w" looks like Greek small omega: ω, whereas Greek big omega is Ω.
2006-10-23 04:21:23 · answer #2 · answered by p_ne_np 3 · 0⤊ 0⤋
check the definitions of each side of the equality:
Γ[W(1)] = (Ω - 1)!
and you will notice that they are the same
2006-10-23 02:20:10 · answer #3 · answered by Anonymous · 0⤊ 0⤋
I'm not sure what you mean by W(1) or Ω in this case. Would you mind defining these terms?
I can, however prove Γ(n) = (n -1)! . . .
2006-10-22 22:51:05 · answer #4 · answered by bag o' hot air 2 · 0⤊ 2⤋
This is just the gamma function by def.
2006-10-23 00:20:27 · answer #5 · answered by mathman241 6 · 0⤊ 0⤋
is 0...W(1)=(1-1)
2006-10-23 04:50:20 · answer #6 · answered by arpalu69 1 · 0⤊ 1⤋
If W(1)=(x-1), then
w1=x-1........................1
therefor,
w1/1=x..........................2
....w=x
2006-10-22 22:52:49 · answer #7 · answered by Lups 2 · 0⤊ 1⤋
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2006-10-22 22:54:03 · answer #8 · answered by big_al225 2 · 0⤊ 2⤋