I want to evaluate central moments of a normal random variable till 8th order. From some search I came to know that for even order ($v$) central moment, it is $Sigma^v*(v-1)!!$ (double factorial) and zero for odd order.
Can some one tell me the expanded final version formula for 4th, 6th and 8th order central moment of normal distribution.
I am confused because from matlab experiment of generating samples from a normal distribution and then finding their central moments is giving me a solution (all 4,6,8 order central moments) which is independent of mean and standard deviation.