B.3 Gaussian Integrals

(September 1, 2023)

We discussed the integrals

I_{n}=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}{\rm d}x\,e^{-x^{2}/2}x^{n}

(B.14)

The first couple results are

I_{0}=1\quad I_{2}=0\quad I_{4}=3\quad I_{6}=15

(B.15)

We found these using the generating function technique.