# Thread: What IS a moment?

1. ## What IS a moment?

Ok, I'm doing a project on the Riemann Hypothesis. And it seems that the first four moments of the zeta-function are 1,2,42, 24024.
But nowhere have I been able to find an explanantion for what the moment of a function actually IS.
Figured this might be a good place to ask

2. Originally Posted by Fintan
Ok, I'm doing a project on the Riemann Hypothesis. And it seems that the first four moments of the zeta-function are 1,2,42, 24024.
But nowhere have I been able to find an explanantion for what the moment of a function actually IS.
Figured this might be a good place to ask
Moments are results of moment generating functions which have the unique properties:

$M_x(t)=E[e^{xt}]$
$M(0)=1; M'(0)=\mu ; M''(0)-M'(0)^2=\sigma$

3. Right - so if 42 is the third moment of the function - does that mean that you just fill in 3 instead of t and you'll get 42 as the expected value of e^3x?

4. Originally Posted by Fintan
Right - so if 42 is the third moment of the function - does that mean that you just fill in 3 instead of t and you'll get 42 as the expected value of e^3x?
$E[X^n] = M^{(n)}(0)$

$E[X^3] = M^{(3)}(0) \Rightarrow 42$