>>725
E[(X-E(X))^(2n)]
= {1/(√(2π)σ)}∫[-∞,∞](x-μ)^(2n)*exp{-(x-μ)^2/(2σ^2)}dx
= {σ^(2n)/√(2π)}∫[-∞,∞]t^(2n)*exp(-t^2/2)dt　(t=(x-μ)/σ)
= {2σ^(2n)/√(2π)}∫[0,∞](2u)^(n-1/2)*exp(-u)du　(u=t^2/2)
= {σ^(2n)*2^n/√π}*Γ(n+1/2)
= {σ^(2n)*2^n/√π}*{(2n)!*√(π)/(2^(2n)*n!)}
= {(2n)!/(2^n*n!)}*σ^(2n)

E[(X-E(X))^(2n+1)]
= {σ^(2n+1)/√(2π)}∫[-∞,∞]t^(2n+1)*exp(-t^2/2)dt　(t=(x-μ)/σ)
= 0　（奇関数）