APPENDIX - Mathematical Formulas - 1

\int_{0}^{\infty}x^ne^{-ax}dx=\frac{n!}{a^{n+1}} \\ \\ \\ { }\hspace{15} \int_{0}^{\infty}x^{2n}e^{-ax^2}dx=\frac{1\cdot 3\cdot 5\cdot \cdot \cdot (2n-1)}{2^{n+1}a^n}\sqrt{\frac{\pi}{a}} \\ \\ \\ { }\hspace{15} \int_{0}^{\infty}x^{2n+1}e^{-ax^2}dx=\frac{n!}{2a^{n+1}} \quad{} (a>0)